"The expectation is that we need to go deeper," Henderson told a news conference in describing GM's restructuring after its previous plan was rejected by the Obama administration. The appearance was the first since Henderson took over as GM's chief executive Monday.
Henderson said he expects the company would "need to take further measures" beyond the five plants it planned to shutter under the original restructuring plan.
Detroit's "Big Three" automakers -- GM, Ford Motor Co. and Chrysler LLC -- have seen sales slump and long-held business models crumble under the weight of foreign competition and a recession-weary economy. On Monday, a White House-appointed auto task force unveiled a tough review of the automakers' recovery plans and called for sweeping new changes if the companies are to receive further federal bailout dollars.
As a sales incentive, both Ford and GM announced payment protection offers Tuesday to attract consumers who may be wary of making a big-ticket purchase when job security is low.
Ford said it will cover payments of up to $700 each month for up to a year on any new vehicle from the company if customers lose their jobs. Henderson made a similar offer, saying the company will make up to nine car payments of $500 each for customers who have lost their jobs through no fault of their own.
U.S. auto sales are at their lowest levels in at least 27 years as tight credit and job losses contribute to a loss of consumer confidence.
"Consumers remain anxious about the economy and their own outlook for the future," Ken Czubay, vice president of sales and marketing at Dearborn, Michigan-based Ford, said in a company statement, reported Bloomberg News.
Ford is also offering no-interest financing through its credit unit.
The announcements came a day after President Barack Obama put tough terms on the recovery plans for GM and Chrysler. The government review included the ouster of GM CEO Rick Wagoner, who had led the company since 2000.
The two auto companies have received $17 billion in federal loans and have requested more government aid to stay afloat. Ford has not yet had to take any federal assistance.
The Obama administration gave GM 60 days to reach deeper concessions with bondholders and the United Auto Workers union and said it would finance a court-supervised bankruptcy if necessary.
Henderson said GM could decide to file for bankruptcy within its 60-day deadline if it became "quite clear" that it would be unable to reach the required deals, Reuters reported.
"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," he said.
As part of the White House review of the auto industry, the government also plans to back new car warranties issued by GM and Chrysler, in an effort to help boost car sales.
"If you buy a car from Chrysler or General Motors, you will be able to get your car serviced and repaired, just like always," President Obama said Monday. "Your warranty will be safe. In fact, it will be safer than it's ever been, because starting today, the United States government will stand behind your warranty."
The program sets up special warranty accounts that will be used only if the automaker runs out of money, reported the New York Times.
South Korea's Hyundai Motor Co. launched a program in January allowing customers to return vehicles if they lose their jobs within the first year after the purchase. The company has out-sold almost all major U.S. automakers this year, as well as other foreign car companies, including Toyota, which have been rocked by the plunge in demand.