GM Chairman and CEO Rick Wagoner, who finds himself under pressure due to battle between Delphi and the United Auto Workers.

NEW YORK (CNN/Money) - The United Auto Workers union has rejected a slightly less severe demand for wage cuts from bankrupt auto parts maker Delphi, raising the threat that the auto parts maker's former parent, General Motors, could have its own operations shut by a strike at Delphi in a month.

The threat is one more problem for GM (Research), whose stock hit the lowest intraday level since 1987 in Wednesday trading and ended nearly 6 percent lower at $21.29.

Top officials with the UAW told reporters Wednesday that a Delphi offer cutting hourly wages by more than 50 percent to $12.50 an hour, rather than its earlier offer of $10 an hour, was "insulting."

"Delphi's contract proposal was not designed to be a framework for an agreement but a road map for confrontation," said UAW President Ron Gettelfinger at a press conference. He also said that Delphi is seeking to eliminate 24,000 of its 34,000 U.S. factory jobs.

Delphi officials confirmed the supplier's proposed new wages and benefits offer, and defended them as competitive when compared with other parts suppliers. The company has said it will seek to have a bankruptcy court judge void a contract unless it reached an agreement with unions by Dec. 16.

The bankruptcy judge can void labor contracts, but Delphi is taking a risk by seeking such steep cuts, according to David Gregory, a professor of labor law at St. John's University in New York. Gregory told The New York Times that the UAW was better off having a judge decide because the concessions Delphi had asked for cut too deep and would probably be thrown out by the court.

"In bankruptcy, the employer generally comes out ahead," he told the paper. "But in this case, I think the UAW will be quite successful."

But if there are wage cuts, the union could go on strike. Since Delphi is still GM's largest parts supplier, a strike could halt operations across the No. 1 vehicle maker. In 1998, GM was essentially shut down by a strike at two Delphi parts plants.

The threat that the union could go on strike after that has sent shares of embattled automaker GM to 18-year lows. GM, which spun off Delphi in 1999, could be responsible for payments of as much as $11 billion due to contract obligations to its former workers at Delphi.

The Wall Street Journal reported Thursday that despite growing shareholder discontent with GM Chairman and CEO Rick Wagoner, he still enjoys the support of the company's board, according to a person familiar with the matter. But directors are speaking with Wagoner on a weekly basis rather than their earlier monthly talks, the paper reported.

Still Wagoner could face new pressure from the board from financier Kirk Kerkorian, who earlier this year bought a 9.9 percent stake in GM at prices between 22 and 43 percent above current prices. In a Sept. 21 filing with the SEC Kerkorian indicated he may seek a seat on the GM board. The Journal reported Thursday that the likelihood of that happening is unclear, but that a person familiar with the matter said "there will be continuing discussions" about the issue.

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For a Fortune magazine's look at the problems facing Wagoner, click here.

For a look at the bankruptcy risk at GM due to the problems at Delphi, click here.

For more news on autos and automakers, click here.