The White House declined to comment on the decision by some General Motors Corp. (GM) executives to sell their shares in the struggling auto maker, but conceded that "there's plenty in GM to worry about."

"It's probably better that I resist the temptation to comment on individuals' personal stock holdings except to say that the president and the auto task force, again, want to ensure the continuation of General Motors and to do so in a way that puts it on that path that doesn't require continued government subsidies," White House spokesman Robert Gibbs said Tuesday.

Late Monday, six GM executives reported the sale of all the company stock they owned. The biggest seller was Vice Chairman Bob Lutz, according to filings with the Securities and Exchange Commission. He sold 81,360 shares for $130,990.

The news helped send GM shares to their lowest level since 1933 Tuesday as investors bet the company is likely to lose its fight to stave off bankruptcy. Chief Executive Fritz Henderson said Monday that a bankruptcy is "more probable."

The company faces a government-imposed June 1 deadline to reach a pact with workers and creditors that keeps it out of bankruptcy court.

Gibbs said President Barack Obama and his automotive task force are still working for a deal that saves the company.

"The task force will continue to work with GM to get a plan that they believe puts it on a sustainable path, while at the same time the president works to improve the economy," the spokesman said.

GM's stock recently traded at $1.10, down 33 cents, or 23%.

Pressed again to comment on the stock sales and the message they send to the public, Gibbs said, "There's plenty in GM to worry about" with the June 1 deadline looming.

-By Henry J. Pulizzi, Dow Jones Newswires; 202-862-9256; henry.pulizzi@dowjones.com