If there is no literal rebirth, why have samvega (a sense of urgency)

It is urgent because suffering is here and now, suffering is real.
You question is like saying " why should I feel urgency to jump out of a fire?" jump now! don't even count on death....

According to Buddhist cosmology (which is based on Hindu cosmology) rebirth as a human is special. It is only as a human you can contemplate "why not live a normal life", as the human realm is the only one on the wheel of rebirth from which buddhahood is attainable:

• Rebirth as a Deva means you're too ecstatic to contemplate Nirvana
• Rebirth as an Asura means you're too angry to contemplate Nirvana
• Rebirth as an animal means you don't have the mental capacity to contemplate Nirvana
• Rebirth as a Preta means you're too frustrated to contemplate Nirvana
• Rebirth as a Naraka means you're too tortured to contemplate Nirvana

Only for human rebirth does Buddhism assert that one is reborn in this realm with vastly different physical endowments and moral natures because of a being's past karma. A rebirth in this realm is considered as fortunate because it offers an opportunity to attain nirvana and end the Saṃsāra cycle.

Why have samvega (sense of urgency that death may strike) without believe in literal rebirth?

You could argue it both ways. Why have sense of urgency if you will be reborn? On the other hand - Why have sense of urgency if you're not going anywhere?

Dharma is called "Safe Bet". Whether there is literal rebirth or not, Liberation is deathless. Whether there is literal rebirth or not, dying without Liberation is scary - because either you may go to some strange inhuman worlds, or you disappear forever.

Hence the sense of urgency to attain Liberation.

A question like this calls for a certain amount of philosophizing, so forgive me if I reach past traditional teachings for a moment.

It seems to me that people tend to approach the question of karma and rebirth from too solipsistic a perspective, thinking of it only in terms of the individual (egoic) self. I understand the motivation behind that: if I feel misery I tend to think of it as my misery, and so I tend to seek out my salvation. It's a natural association in the mind.

But karma strikes me as transpersonal: as something that moves through the egoic self, not something affixed to the egoic self. I mean, if we look at someone we might characterize as cruel — be it an abusive spouse or a brutal dictator — what we mean by 'cruelty' is that this person has attachments that drive him/her to inflict misery on others. That cruelty pervades the space around h'er, spreading outward, and finds resonances with the people and things it encounters. One can say the same about any strong attachment. It isn't merely a question of misalignment with reality that an attachment implies, but also a question of how that misalignment reflects back on the reality it is misaligned with. Like throwing a stone into a pond, an attachment sends ripples out in waves long after it has disappeared from sight.

The upshot is that we do not merely create 'mind dwellings' for ourselves. We create mind dwellings and impose them on the world around us, implicitly demanding that everyone and everything around us share them. Someone who is angry and resentful creates asura loka and tries to draw others into it; someone who is fearful or depressed creates peta loka and tries to draw others into that; someone who behaves as an animal does creates... You get the idea. And when we create these mental realms and draw others into them, we create a resonance (an echo of those mental attachments) that extends beyond our reach in time and place. In effect, we recreate our egoic selves — our attachments, our cravings, our miseries — in others by imposing our mental realms on the world around us, and drawing those others into it.

In this sense, it isn't 'us' who reincarnate, it is these mental realms (egoic states) that reincarnate, reforming themselves in others because of the resonances we leave in our wake.

The dharma, then, becomes a tool for countering this karmic process. We release attachments so that we do not echo them outward into the world; we seek higher states to help absorb what dukkha is presented to us by the world. We do not pass on karma to others — neither making it on our own nor allowing it to pass through us — and so our egoic selves pass on into oblivion.