WASHINGTON/DETROIT – General Motors warned on Tuesday there was a rising chance it could file for bankruptcy by June as Fiat and Chrysler executives met in a race to complete a tie-up the U.S. government has said Chrysler needs to survive.

GM shares tumbled 28 percent, its bonds fell and the cost to insure its debt rose, as the markets began to price in a bankruptcy that could wipe out stock holders and force deep losses on other creditors, even under the quick and surgical process described earlier by U.S. officials.

GM and Ford Motor Co, which has not sought a bailout, announced incentives to woo recession-wary customers by covering some car payments for customers who lose their jobs.

U.S. auto sales for March are expected to have fallen 40 percent from a year ago when sales data is released on Wednesday.

In Detroit, GM and Chrysler began work to implement the tough restructuring dictated by the Obama administration as a condition for providing more taxpayer funds to the struggling automakers.

Fiat Chief Executive Sergio Marchionne flew to Detroit for talks with Chrysler's labor unions and creditors after President Barack Obama gave the companies 30 days to set up a partnership to save the ailing car group.

Advisers to both GM and Chrysler have also been working in parallel to prepare for potential bankruptcy filings that would aim to preserve the best elements of the struggling companies while slashing debt and cutting pension and health care costs.

BANKRUPTCY OPTIONS

One possible plan under discussion for GM would quickly form a new company representing the automaker's best assets while its laggard brands and money-losing assets would remain under bankruptcy protection, a person familiar with the strategy told Reuters.

GM stock has lost almost half its value since Monday when Obama outlined policies sharply limiting taxpayer funds for automakers that many had expected him to rescue.

Chief Executive Fritz Henderson -- installed in the job on Monday in a shake-up that included the GM board -- said the top U.S. automaker would have to close more plants and shed more factory jobs than it planned just a month ago.

We need to go deeper and we need to go faster, Henderson told a news conference at GM's Detroit headquarters.

His predecessor, Rick Wagoner, was forced out by the Obama administration, which gave GM 60 days to reach deeper concessions with bondholders and the United Auto Workers union. The U.S. Treasury would finance a court-supervised bankruptcy for GM if the process failed to deliver enough savings.

By no later than June 1, if we're not able to accomplish this outside bankruptcy, we'll be in bankruptcy. It's pretty clear. The government was unequivocal, Henderson said.

'PENNIES ON THE DOLLAR'

Bondholders, a key constituency in the GM restructuring, said they were braced for a reduced offer of pennies on the dollar for about $28 billion in GM debt.

GM last week had offered bondholders about $6.5 billion in cash and new debt -- equal to a combined 24 cents on the dollar -- in addition to a 90-percent stake in the new company, a person with knowledge of the terms sheet told Reuters.

The $13.4-billion emergency loan for GM approved by the Bush administration in late December had offered bondholders a payout of 33 cents on the dollar in equity, terms that they had rejected.

GM's 8.375-percent bonds due 2033 were trading on Tuesday at 12.75 cents on the dollar, according to MarketAxess.

Bondholders have to understand that they have to come to the table. So far they've held back. There's no holding back anymore. In bankruptcy, they'd likely come away with nothing, said Representative Sander Levin, a Democrat from Michigan.

Standard & Poor's on Tuesday cut its ratings on Fiat to junk status and said it may cut them again, citing weak liquidity and upcoming debt maturities.

Fiat investors have worried that the company could end up contributing cash or debt guarantees to the Chrysler partnership at a time when its own finances are strained.

Chrysler, privately held by Cerberus Capital Management, has been surviving on a $4 billion emergency loan from the U.S. government.

Fiat has agreed to contribute access to its small-car technology and vehicle platforms to Chrysler in exchange for a stake in the U.S. automaker that would start at 20 percent.

We do not expect Fiat to commit any significant funds to support Chrysler following the U.S. government's most recent analysis of Chrysler's financial needs to survive, S&P said in a statement. Still, we expect more details in the coming weeks on the proposed Chrysler-Fiat alliance.

LOSE THE JOB, KEEP THE CAR

GM and Ford said they would cover some car loan payments for customers who lose their jobs, an offer aimed at consumers sidelined by the recession and worried about job security.

GM said it would cover nine payments, up to $500 per month, if GM car buyers lost their income. Ford will cover payments for up to a year if customers lose their jobs.

Both programs, being offered in addition to zero-percent financing, come at a time when U.S. auto sales are at their lowest levels in nearly three decades.

South Korea's Hyundai Motor Co has outperformed rivals in the slumping U.S. market after launching a program in January that allows laid-off workers to return cars they financed.

Hyundai's sales rose 5 percent in the first two months of the year while overall U.S. sales tumbled 39 percent.

(Additional reporting by John Crawley, Emily Chasan, Walden Siew and David Bailey)

(Editing by Patrick Fitzgibbons and Tim Dobbyn)