NEW YORK (CNNMoney.com) - General Motors is stockpiling parts in preparation for a possible strike at parts supplier Delphi, according to GM Chairman and CEO Rick Wagoner, but he conceded the company will not be able to operate if there is a prolonged job action there.

The United Auto Workers union has threatened to strike Delphi, the bankrupt parts maker that is GM's largest supplier, if Delphi uses bankruptcy court to void its current union deals. On March 31, Delphi asked the bankruptcy court for the right to get out of its labor pacts.

GM Chairman and CEO Rick Wagoner.

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Wagoner appeared on the CBS interview show "Face the Nation" on Sunday. In answer to a question about whether GM (Research) is stockpiling parts in preparation for a Delphi (Research) strike, he responded, "we're doing some of that," although he quickly conceded, "We could run for a while, but we can't run for a significant period of time," if there is a strike at Delphi.

But Wagoner repeated his past statements that he believes an agreement will be reached between GM, Delphi and its unions to avoid a long strike at Delphi, saying there's too much at stake for any of the sides to allow it to happen.

"And that's why I continue to think, 'Shame on us, the leaders of all those groups, if we can't come to a solution that avoids that kind of drastic action," he said.

Wagoner also repeated his often stated position that a bankruptcy filing is not the way to go for the world's largest automaker, even if many analysts believe the company will eventually file for such protections.

Asked if a strike at Delphi would kill GM, he responded, "A long-term strike at...Delphi would have huge ramifications for General Motors, for other (automakers), for the unions that represent workers, and for Delphi."

Wagoner praised the leadership of the UAW for willingness to work on cutting health care costs and take other steps to trim costs.

Wagoner also said he believed he would continue to have the support of Kirk Kerkorian, GM's largest individual shareholder, for the moves the company is making. He also does not believe the company will need or receive any kind of federal bailout.

"The message has been clear, and we've been working on solving our own problems," he said.

For more on Delphi's move to shed its union contracts, click here.