Did Joseph Goebbels really say this about German opposition in 1933?

No, most probably not. On that day Goebbels was silent in public, and the entire text looks made up.

Proving a negative is very difficult, and currently this 'funny propaganda meme' lacks an accurate transcript, lending this quest easily to misunderstandings, mishearings, mistranslations between Russian, English and German language alone. But: We can be very certain that this or anything close to this was not said by Goebbels in any of his better known speeches, and very certainly not on the given date of March 12 1933.

This is one day before Goebbels became minister of propaganda, and that year's Volkstrauertag the national holiday 'people's day of mourning'. That day a memorial ceremony was held in Berlin, with Hindenburg and Hitler at the centre, then Hitler gave a radio speech, Goebbels in studio beside him, but silent. Then Hitler flew to Munich giving another speech to his comrades, while Goebbels phoned his mom, talking about the national revolution and local elections. Documented in this way in his diary for this day:

12 March 1933 (Kaiserhof)
In the Lindenoper we commemorate the fallen of the great war. The Reich President enters the large box. He seems almost like a mythical monument. Hitler and Hindenburg, symbols of youth and age, joined hands in these two men. Outside, in glaring sunshine, the Reichswehr, S.A. and Stahlhelm march past Hindenburg. A colourful picture of a magnificent parade. I drive back to the Reich Chancellery with the Führer and stand next to him as he, trembling with excitement and solemn emotion, reads out over the radio the proclamation to the German people, according to which the new flags will rise over the German nation. I feel as if a shiver of history is passing over us. The Führer flies to Munich to personally discuss the most urgent Bavarian issues with the responsible party offices. In the evening we get the results of the local elections. We have broken the red majorities in all cities, even in Berlin. This is an unparalleled triumph. Now the sentence: Berlin remains red! is ad ab surdum. Even in the blackest strongholds we are gaining ground across the board. It's so unbelievable that you can't believe it at the moment. I phone home late at night to my mother. She can hardly speak for emotion. We sit in the editorial office of the "Angriff" until dawn and discuss the future of Berlin. I delegate Dr. Lippert as temporary commissioner. We will reshape this city. Our whole ambition will be to give it a German face again. We want to work until we drop. None of us will spare ourselves. We want to go to work with all our dedication.

— Ralf Georg Reuth (ed): "Goebbels Tagebücher 1924 -1945", Piper: München, Zürich, 1992, p778.

With the date firmly excluded, we now see the vocabulary and diction as awkwardly un-Goebbels over-all, with the themes mentioned not really matching the date or other dates close to it, nor really any date, either.

For completeness sake, we can also exclude that the host in the meme might have conflated Goebbels with Hitler while still getting the date right: Hitler's radio speech and his short address in Munich are documented, and neither mentions anything from this quote. His radio speech centres around his accomplishments, some thanks to loyal soldiers, the new constitution-violating swastika flag, some orders to his comrades, and the public warning to party members, foremost the SA:

But beware of provocateurs and informers who, as we know today through evidence, have been sent into our formations by the communist party!

— Max Domarus: "Hitler. Reden und Proklamationen 1932–1945", Pamminger: Leonberg, 1973, p221

At the time given, the regime's and especially Goebbels' rhetoric was hardly about any "opposition" and even less so about "opposition figures". These words would match better his parliament speeches pre-1933 or much later 'looking back' speeches.

During the consolidation phase of taking power in early 1933 his rhetoric was about 'unity' and 'building', 'solidarity', including, and persuading the remaining 'doubters'. They 'were all in this together' (except of course some 'evil people').
If any 'opposition figures' were mentioned, then it would have been either vague code or easily identifiable 'othering' as in the concrete: communists, marxists, bolsheviks, with not even the equally hated social-democrats directly named as opposition. The first groups were to be excluded permanently, while their voters/supporters and the social-democrats were to be integrated into the Volksgemeinschaft.

Compare the speech he gave on March 15 1933:

On the contrary, [the government] must make all propagandistic preparations to win the whole people over to its side. If this government is determined never to give way, never, ever and under no circumstances, then it does not need to use the dead power of the bayonets, then it will not be satisfied in the long run with knowing that 52 per cent are behind it in order to terrorise the remaining 48 per cent, but it will see its next task in winning over the remaining 48 per cent for itself.

— "Deutsche Geschichte in Dokumenten und Bildern", Band 7. "Deutschland unter der Herrschaft des Nationalsozialismus 1933–1945", Joseph Goebbels: Zwei Reden über die Aufgaben des Reichsministeriums für Volksaufklärung und Propaganda (15./25. März 1933) (PDF)

'Foreign financiers of opposition groups' was not only not on the agenda at the time, the very terms "from the West" don't fit the speech regulations he imposed onto himself. He would have used antisemitic code, like perhaps "international" or "intellectual", or directly name "Jews", or even entities like "France" — despite the nazis this early mostly avoiding stirring up too much ruckus with 'actual enemies' beyond their German jurisdiction, that could take offence when the regime was this insecure at the beginning of 1933.

It is also strange to read "USA", when Goebbels used that word, but seldom, preferring "Amerika" most of the time, whether in speeches or interviews. With not too less of admiration in many early interviews even. Therefore this strange word "trans-oceanic", which I couldn't locate in any of his speeches anyway seems especially misplaced.

This all looks quite like not even a conflation of any sort. It looks like an invention from whole cloth. The only part of a phrase I would place into this horse's mouth would be the one with "mud":

Q: Opposition figures throw mud at our country.

While we do find this near the alleged date of the 'quote', but within the context of 'art', not political opposition (albeit of course that art was political):

Things have happened in Germany in these fourteen years which - of this I am firmly convinced - in twenty or thirty years' time will only cause people in Germany to shake their heads, — Things that we accepted in the psychosis of November, things about which those in the know in the country were sad and grieved and shaken, but which the people accepted without perhaps giving them much thought, things in the field of politics, art, theatre, the press, even broadcasting, which, if one were to compile them again in the archives after twenty years … [unintelligible] … a spirituality that was actually no longer a spirituality at all, the spirituality of asphalt, detached from any responsible bond. A spirituality that no longer had anything to do with the people, that acted as if it were there alone and a people did not exist at all. Thus the radio, thus the press, thus the cinema, thus the theatre became a threshing floor for the spiritual excretions of an asphalt nomadism that had become completely rootless, that forced its spiritual products on the people and whose spiritual products the people accepted for lack of something better and because the people had completely lost the concepts of spiritual and unspiritual, of great and small, of valuable and worthless under the psychosis of November.

In this spirituality of the asphalt, the mob instinct was running riot - the mob instinct of the most inferior kind.

All the great ideals that existed in Germany were kicked into the excrement, distorted, dirt was thrown at them, they were bad-mouthed to the people.

Thus the people were deprived of their ideals, they were no longer to believe in greatness, in boldness, in heroism, in violence. Not without reason did the men of November do this, because they knew very well: as long as the people still had a possibility of comparison between the past and the present, they were bound to fail before this comparison. Because the present had been so fabulously small since 1918, the greater past had to be removed from the people's field of vision, all great memories had to be lied away from the people, so that they, wallowing in these great memories, could not recognise the dreadfulness of the present.

— 25.3.33 – Berlin, Haus des Rundfunks – Ansprache an die Intendanten und Direktoren der Rundfunkgesellschaften («Die zukünftige Arbeit und Gestaltung des deutschen Rundfunks»), translated & quoted from: Helmut Heiber: "Goebbels. Reden 1932–1945", Gondrom: Düsseldorf, 1971, p82. Translation & paragraph in italics LLC. Online version from comment by @Mark Johnson)

Noteworthy: In this speech he mostly characterises the 'nazis as 'in the opposition' for 14 years, after the from content and context very different 'men of the opposition' (the democratic 'fifth column' of the second Reich, Jews, marxists, social democrats, and what-all-else he saw as 'the enemy of the people'…) overthrew the monarchy in November 1918.

In the same style Goebbels characterises mud/filth in his speech for a book burning:

10.5.33 – Berlin, Opernplatz – Bücherverbrennung auf der Kundgebung der Deutschen Studentenschaft 'wider den undeutschen Geist'

But this is what distinguishes this revolution from the revolt of November 1918, when materialism broke through and Marxism took the field. The forces of subhumanism conquered the political terrain, and this was followed in Germany by fourteen years of unthinkable and indescribable material and spiritual disgrace. We all felt this ignominy in our own bodies. Every worker who lost his place at the machine felt it. It was felt by every young worker who was excluded from access to work. It was felt by every citizen who had his last penny taken out of his pocket. It was felt by every soldier who, gritting his teeth, had to watch the national defence and the honour of the German people being trampled on with impunity.

You students also felt it, you who were driven down from the universities as the vanguard of a truly revolutionary German spirit, you who were beaten with rubber truncheons when you sang the Deutschlandlied or protested against Versailles, you who had to endure the humiliations of this November Republic for fourteen years in silent shame.

The libraries were filled with the rubbish and filth of these Jewish asphalt literati.

Instead of German education educating the German people in Germany, and instead of real leaders of the people speaking the spirit of the times from the pulpits of the universities, high science entrenched itself behind the paragraphs and behind the bundles of files and behind the pandecs. And while science gradually isolated itself from life and allowed itself to be cut off, the young Germany had long since restored a new and finished state of law and normality.

This state of law and normality, of which we were the bearers in the opposition movement, has now, with our assumption of power, also become the state of law and normality of our state. The movement that ran over the state at that time has now marched into the state - yes, even more: it has become the state itself! And the men who led this movement against the state at that time are now the holders of state power.

— Heiber, see above, p108.

This small but stable idiosyncrasy about 'who was opposition when' aside, and also excluding the mentioning of dirt/mud, the rest of these lengthy speeches show very, very little resemblance to the quote supposedly sought. The speeches from 1933 are hardly even a credibly source for cobbling together the pastiche creation we're looking at.