Does being in a commited married life make it impossible to attain Nirvana? If not, how can one progress towards Nirvana?

The topic of if householders or laypeople can attain Arahantship is highly debated. There is a list of laypeople having attained Nibbāna in AN 6.119-6.139, but this is a very isolated scripture which could have been a later addition.

The usual consensus it that a householder is capable of attaining the path anāgāmi or non-returner, but that Arahantship is highly unlikely. If Nibbāna is possible for someone committed in a marriage? By deduction, you could say is very highly improbable.

I think that rather than focusing on Nibbāna, you should concentrate on the path of stream entry (sotāpanna). Even that is very difficult to attain, let alone Nibbāna. Once you do reach sotāpanna, you will then have other things to worry about. :)

Anapanasati(mindfulness of breathing)meditation technique is given by the Buddha for the lay men/women married life. One can practice this while doing household chore. As a stream entry, there is still attachment for his/her spouse, only three fetters got rid of. Then if progress to be a Sakadagami, this attachment for the spouse just lessen, still not get rid of. Only at attaining Aanāgāmi, no more attachment to spouse still need not to be a monk.

No, being in a commited married life does not make it impossible to attain Nirvana.

Being in a commited married life helps you towards reaching Nirvana.

Suffering always helps you reach Nirvana.

When suffering is present, commited married life can arise. When commited married life arises, good action and bad action towards liberation arise. When good action arises more than bad action, knowledge leading to liberation rises. When knowledge leading to liberation has rised enough, liberation follows. When liberation follows, suffering has come to an end. When suffering comes to an end, compassion for suffering of other beings is arised. When compassion for suffering of other beings is arised, only good action towards these beings is arised. When good action towards beings is arised, your strive to help these beings become liberated is arised.

If suffering comes to an end while being in a commited married life, your strive to help your woman (or child, or family,...) reach liberation is arised. Sometimes this means ending the relationship. Sometimes it means staying in the relationship.

You see, when you reach Nirvana while being in a commited married life, it's like reaching Nirvana while being a butcher in your own farm (the case is extreme, but it is not impossible). When you reach Nirvana while being a butcher in your own farm, what do you do with your animals? Yes, you stop killing your animals. But, do you let them go? No, because letting them go, would be the same as killing them, as they don't know how to survive because they were domesticated by you. So, you decide paying the price for your past bad actions - you stay with the animals, feed them, nourish them, teach them how to survive, help them towards their strive to end their suffering. Only after you've done everything you could to help your animals, you let go of them. Only a liberated mind can know when he has done everything he could to cleanse his past deeds. Once you let go of them, you never, ever, build your own farm again.

In the Gihi Sutta (Householder Sutta), the Buddha said:

"Sariputta, when you know of a householder clothed in white, that he is restrained in terms of the five training rules and that he obtains at will, without difficulty, without hardship, four pleasant mental abidings in the here & now, then if he wants he may state about himself: 'Hell is ended; animal wombs are ended; the state of the hungry shades is ended; states of deprivation, destitution, the bad bourns are ended! I am a stream-winner, steadfast, never again destined for states of woe, headed for self-awakening!'

You may read the sutta for details of the five training rules and four pleasant mental abidings. Basically, it means that a householder can definitely reach at least stream entry, which is the first stage of enlightenment. After stream entry, he will attain Nirvana within seven rebirths, either as a human or in higher realms.

You can remain a married householder with responsibilities, but you need to slowly get rid of the fetters which are all within yourself and not in the people or situations around you. It's in your mind and heart, not in your life situation. Getting rid of the fetters is related to the fourth pleasant mental abiding. The importance of intention can be seen in this answer, where the hunter's wife is a stream winner who is free from the sins of her husband's profession, because she does not harbour any ill intentions and only fulfills her responsibilities as his wife.

For e.g. if your loved one passes away, you may grieve deeply for a long time, but, if you understand intellectually and subconsciously that nothing is permanent, then you can accept it easily and move beyond it quickly. This is possible when one has progressed well along the path.

When one is still new on the path, as suggested by @ChrisW in his comment with this story, marriage and the lay life of a householder can provide stimuli e.g. in the form of grief in order to prod one towards the path to enlightenment.

You can find many more relevant advice from the Buddha for lay persons on how to manage finances and on many other topics, in the Sigalovada Sutta. These can be considered additional guidance on the path to enlightenment.

I also enjoy the conversation between the Buddha and Dhaniya the cattleman-householder in the Dhaniya Sutta. A small part at the end quoted below. But you should read the whole thing - it's very good.

The Buddha: "Having broken my bonds like a great bull, like a great elephant tearing a rotting vine, I never again will lie in the womb: so if you want, rain-god, go ahead & rain."

The great cloud rained down straightaway, filling the lowlands & high.

Hearing the rain-god pour down, Dhaniya said: "How great our gain that we've gazed on the Blessed One! We go to him, the One with vision, for refuge. May you be our teacher, Great Sage. My wife & I are compliant. Let's follow the holy life under the One Well-gone. Gone to the far shore of aging & death, let's put an end to suffering & stress."

how someone can be in a commited relationship and at the same time achieve nibbana

I had a dream recently in which my wife went out for the evening without me: I was jealous, craving her and self-centred (wanting her to pay attention to me instead), clinging (wanting to not to lose her, wanting to not lose or to repeat the happy experience/relationship I had earlier with her), and averse to the situation (not wanting to be left alone), and angry (with her for making the decision to go out without me).

Because I was jealous and so on I was unhappy. Even when she came home she still seemed unhappy and avoided me.

Then I thought (after I woke up), maybe it's because I was unhappy like that she wanted to go out without me. Who wants to spend time with some unhappy man? Can you even ever satisfy someone who is craving and clinging?

Our relationship would be better if I were happier in myself, more "unconditionally" happy ... or more possessed of equanimity and metta and less of ego and so on. Then when she came home I could say, "Oh, nice to see you, how are you?" and so on and be a better friend.

a commited relationship is bound to have a multitude of attachments

Perhaps it's helpful to distinguish between "attachment" and "responsibility".

For example maybe you have a responsibility to try to help your children, feed and educate them.

When I was first born my father wanted me to grow up to be a good cricket player: that was his ambition, he put a cricket bat in my cradle, etc. I tried cricket a few times (he played) but not very often. It's probably best that he wasn't too "attached" to the idea of me becoming a cricket player.

In this answer yuttadhammo wrote,

In brief, duty and responsibility should be what dictate our worldly affairs, not concern or care.

advice for marriage partners

In the book I mentioned in this answer the author tries to summarize the Buddha's advice for laypeople. Chapter 6 of that book is about "establishing a marital partnership" and includes the following advice:

For him:

1. Show respect to her
2. Refrain from words that might hurt her
3. Practice faithfulness
4. Give up dominance
5. Respect her fondness for beauty

For her:

1. Work in an organized way
2. Handle family relationships
3. Be faithful
4. Take steps to protect the family wealth
5. Show skill and energy
6. Play an active role as his companion and guide

Te book mentions that a lot of Buddhist literature is written by and for monks, and that the role of lay people in society isn't the same as monks'.

Chapter 5 of that book suggests that your partner should be someone who might help your own spiritual progress and life.