Top GOP congressional leaders have privately discussed shopping a tax cut of roughly $350 billion to members this week, after two Republican senators informed President Bush and Vice President Cheney they will not sign off on a bigger tax cut, according to party officials.

Bush had called for a $726 billion tax cut package, which the House accepted. But the Senate first whittled it to $626 billion, then $613.2 billion. As the costs involved in the war with Iraq became clearer, the Democrats succeeded in whacking the cut to $350 billion. Now the tax cut goes to conference, with the two chambers struggling to reach an agreement over its size.

While Republicans continue to fight for a tax cut of $500 billion or larger, a key House GOP leadership aide said Speaker J. Dennis Hastert (R-Ill.) may be forced to talk to House conservatives about a much smaller one. GOP leaders are scrambling to find spending offsets to justify a bigger tax cut, but "we might not be able to pull it off," the aide said, basing his comments on conversations among the speaker's staff late last week.

This pessimistic assessment follows an unpublicized meeting at the White House last Thursday. As budget talks hit a fevered pitch, Bush and Cheney took a break from the war and called over Hastert and Senate Majority Leader Bill Frist (R-Tenn.) to discuss the tax cut with Sens. George V. Voinovich (R-Ohio) and Olympia J. Snowe (R-Maine), two key holdouts.

Voinovich and Snowe made it clear they would not support a tax cut bigger than $350 billion or any budget resolution that calls for one, according to sources familiar with the meeting -- unless the White House comes up with hard-to-find offsets. White House officials and House GOP leaders thought Snowe might bend to pressure, but two Senate sources said Frist has been telling them for weeks she would not. In the meeting, she refused to back down, the sources said.

In the Senate, where Republicans hold a 51-49 majority, Voinovich and Snowe have the power together to bring down the GOP budget if they oppose the tax cut amount because Sens. John McCain (R-Ariz.) and Lincoln D. Chafee (R-R.I.) are against it, too. Bush continues to demand his $726 billion plan, including elimination of the tax on stock dividends. Hastert and Frist are pushing a cut around $550 billion, allowing for a scaled-back version of the Bush dividends plan.

Voinovich "has been very insistent that he wants a tax cut of $350 billion," said his spokesman, Scott Milburn. "He thinks it's a reasonable number and provides a good stimulus." Milburn said Voinovich has no plans of backing down.

So, Republicans could be headed for a budget train wreck. A top House GOP aide said several dozen House conservatives have said privately they will vote against any budget that calls for a tax cut under $500 billion. House Majority Leader Tom DeLay (R-Tex.) has raised the possibility of delaying the adoption of a budget resolution until after the spring recess to allow cooler heads to prevail.

"The speaker . . . does not believe we could pass a tax cut as low as $350 billion," said Hastert spokesman John Feehery.

FOOD BREAK: The bill had everything its sponsors could want: broad support, powerful sponsors, no apparent opposition and a politically appealing message. But it kept getting delayed, sidetracked or trampled by controversial causes. Now its backers are gearing up again -- and hoping for better luck.

The initiative, sponsored by Sens. Richard G. Lugar (R-Ind.) and Patrick J. Leahy (D-Vt.), would increase the tax deduction for corporations when they donate food for the needy and extend the deduction to unincorporated businesses -- farmers, restaurants and others -- that do not now qualify for the tax break. The idea is to cover the cost of packaging and distributing the food, thereby encouraging donation instead of destruction.

The bill was passed by the Senate in 2000, only to be wrapped into a broader tax bill and then stripped out as extraneous. Over the next two years, sponsors tried to hitch it to other tax, farm and charity bills, without success.

Now the charity bill is back before the Senate, shorn of "faith-based" provisions that stymied it in the last Congress, and headed for passage. House leaders have indicated support.

THE WEEK AHEAD: The hottest action on the Hill this week will take place behind closed doors, when congressional leaders hash out a final budget resolution and a supplemental bill to fund the Iraq war. The House and Senate are expected to quickly approve about $80 billion for the war, homeland defense and aid to U.S. allies. Bush wants the bill on his desk by Friday. Staff writer Helen Dewar contributed to this column.