Fritz Henderson told the court that if the sale is not approved by July 10 and GM loses access to government funding, the company would be forced to liquidate.
He testified on the first day of a hearing at which the carmaker is seeking court approval for the sale just 30 days after filing for Chapter 11.
"Business is doing better" at GM, Mr Henderson said, as customers, suppliers, workers and others anticipate the completion of a successful deal. He added that the company had originally hoped to repay its loans to the government and restructure outside of bankruptcy.
Mr Henderson said during questioning that while sales in June were not as bad as expected, they were still down.
"We do not expect to make money in June of 2009," he said.
Part of the reason business is better is the success of Chrysler's asset sale out of bankruptcy, Mr Henderson said.
"The 363 transaction with Chrysler did go relatively quickly. It provided some buyers assurance that this can go relatively quickly," he said.
Mr Henderson also discussed the ouster of former GM CEO Rick Wagoner, saying that Mr Wagoner told him that he had been asked to step down by Steve Rattner, head of President Obama's autos task force.
The GM sale hearing, before Judge Robert Gerber, is expected to continue for at least two days, as the company faces objections and questions from its creditors committee, a group of dissenting bondholders, those with liability and asbestos claims against the company, as well as unions and dealerships.
If the deal is approved, GM will be able to sell its best assets, including Chevrolet and Cadillac, under Section 363 of the bankruptcy code to a "New GM" while the US Treasury would provide billions of dollars in financing.
GM's old assets would remain behind in bankruptcy court to be liquidated.
A successful sale would mark the second big victory for the Obama administration's autos task force, which earlier this month also helped broker the sale of Chrysler LLC to a group led by Italy's Fiat SpA. The US Supreme Court cleared the way for that deal to go through on June 9.
Mr Henderson said during questioning by GM's lawyer that the company spends US$26 million a month to pay the benefits to members of several unions that have about 150 active employees in the company.
No competing bidders have emerged as an alternative to the US government's US$60 billion financing for GM, including a proposed equity investment of US$50 billion that would give the US Treasury a 60 per cent ownership stake.
Under the plan, the United Auto Workers union would gain a 17.5 per cent stake in New GM, the Canadian government would own about 12 per cent, and GM bondholders are expected to get about 10 per cent.
GM has said more than 50 percent of its bondholders support the deal, but a group of small bondholders mounted a challenge to the sale in court on Tuesday.