As a long-time turnaround professional, I deal all the time with companies which only have enough cash left to maintain operations for a limited number of months.
It is a setting which requires intense focus, an unrelenting sense of urgency, and the ability to take decisive actions on many, many fronts – usually all at the same time – in an effort to restructure operations and survive.
Which is why this is simply irresponsible talk:

A top executive of Chrysler LLC cautioned Wednesday that a carmaker collapse could send the economy spiraling into a depression, as the United Auto Workers union braced for contract concessions.
Jim Press, Chrysler’s vice chairman, said the U.S. automakers were “down to months left,” as industry officials ratcheted up a fierce lobbying push to persuade Congress to approve as much as $34 billion in emergency aid.
“We’re on the brink with the U.S. auto manufacturing industry,” Press told The Associated Press in an interview. “If we have a catastrophic failure of one of these car companies, in this tender environment for the economy, it’s a huge blow. It could trigger a depression.”

No, the American auto industry is not on the brink. The unionized Detroit auto industry is on the brink. And until their management and unions have the backbone to make themselves cash flow positive and cost competitive with the rest of the vehicle manufacturers operating in the USA, they will fail and deserve to do so.
The article continues:

Under consideration were the possibility of scrapping a much-maligned jobs bank in which laid-off workers keep receiving most of their pay and postponing the automakers’ payments into a multibillion-dollar union-administered health care fund.

If the Big 3 were serious about surviving as economically viable companies, they would not be addressing these issues only now, at the last minute.
The article continues:

…[Henderson, president and COO of General Motors said]…choosing the bankruptcy route would further erode consumer confidence in the automaker and “we want them to be confident in their ability to buy our cars and trucks.”

If consumer confidence is eroding, it is because Americans have grasped the now-obvious fact that other auto manufacturers have come to America and shown it is possible to run profitable domestic manufacturing operations but Detroit only knows how to whine for corporate welfare funds as they lose money.
There are plenty of valuable assets in the Big 3 – trained workers, facilities, physical materials, etc. Those assets don’t go away in a bankruptcy. Rather, someone who is more capable of thinking outside the box will figure out how to deploy them economically. Bankruptcy gives such new actors the time to figure out a new business model which is cash flow positive – including the right to reject contracts which inhibit implementation of such a model.
More here.
ADDENDUM
The Big 3 spent $50 million on lobbying Washington politicians in the first 9 months of this year and gave another $15 million in campaign contributions to politicians.
Think if they had spent that money instead on restructuring professionals and figured out how to make their businesses cash flow positive instead of begging politicians for more corporate welfare.
These are just the latest two examples of why they deserve NO bailout monies.
ADDENDUM #2
Don Boudreaux offers these thoughts:

Detroit auto executives advocate “government getting a stake in the auto companies that would allow taxpayers to share in future gains if they recover.”
I remind these executives that each American is already perfectly free and able, with no action from government, to “get a stake” in these companies. Of course, few Americans now choose to do so – a fact that reflects the considered judgment of millions of people that these companies are unworthy recipients of investment funds. If millions of investors, spending their own funds, refuse to invest in GM, Ford, and Chrysler, why should Congress force them to make such investments? Why should we trust that Congress will make wiser investment decisions with other people’s money than these people themselves make with their own money?