Treasury Secretary Tim Geithner stopped short on Tuesday of promising that President Obama would veto any legislation that extends tax cuts for top earners.

Geithner said that while he's optimistic the administration will succeed in pushing lawmakers to extend most of former President George W. Bush's signature income tax cuts, he would not pledge a veto if that bill also extends tax cuts for the nation's highest earners.

Obama has said he favors extending the tax cuts except for households earning more than $250,000 per year and individuals making over $200,000 per year.

"What the president believes is the best strategy for the country is to extend the tax cuts that go to more than 95 percent of Americans, more than 95 percent of small business," Geithner said on "Good Morning America" on ABC. "But to do that responsibly, we let those tax cuts for the highest-earning Americans expire as scheduled, as they were predicted to do."

Political wrangling could make allowing the top tax rates to spring upward difficult for lawmakers, who are reluctant to be seen as raising taxes in the midst of a recession.

Republicans have called for the extension of all of the tax cuts — though some conservatives admit this may be unrealistic — and some Democrats have joined them. Other Democrats have called for a temporary extension of the high-end tax breaks.

Geithner said the administration strongly supports ending the tax cuts for wealthier taxpayers, but would not commit to a veto promise.

"I would be happy to give veto on so many things," Geithner said. "You have no idea."

But he said no when asked if he were willing to pledge a veto over the tax cuts.

As for when lawmakers might approach the matter, Geithner said they'll have to decide, though a resolution is unlikely until after the election.

"The leaders of the House and the Senate have to decide when they move. Some people think the House should move before the election. Senate will follow," he said. "Some people have other ideas. But most people don't think you're going to see the legislative outcome finished on this until after the election."

That timeline puts lawmakers in the difficult position of possibly finishing action on the tax cuts during the lame-duck period between Election Day and early January, when the new Congress is sworn in.

All of the tax cuts expire at the end of the year, meaning that if Congress does nothing, most people's tax rates will be raised.