A handful of Senate Republicans are infuriated with their leaders for the way President Bush's tax cut was handled before a budget resolution vote last week.

The anger has not yet reached the level of a revolt but it has become a problem for new Senate Majority Leader Bill Frist of Tennessee.

South Carolina Sen. Lindsey Graham, who voted for the non-binding budget resolution and $350 billion tax cut last week attached to it, said he will oppose any tax cut that small when the tax cuts come up for a vote later in the year.

Graham is blasting Frist, Majority Whip Don Nickles of Oklahoma and Senate Finance Committee Chairman Charles Grassley of Iowa, accusing them of violating a deal that Republicans in the Senate, House, and Bush administration were counting on to get the biggest tax cut possible.

Bush had wanted a $726 billion tax cut, but with Democrats and moderate Republicans saying the cut is too big during times of war and deficit, Republican leaders began looking for the best alternative they could get.

The deal they had reached was for the Senate to approve the budget resolution with a $350 billion tax cut to be approved later this year while the House would pass a $626 billion cut. The differences between the two versions were to be settled during a conference between Senate and House negotiators that Republicans hoped would bring the number up to $550 billion. 

But just before the vote, Grassley announced a different deal that he said had Frist's approval.

"I agreed that I would not return from conference — let me emphasize, I would not return from conference on the growth package —  with a number larger than $350 billion in revenue reductions," Grassley said in what appeared to be an effort to get moderates Republican Sens. Olympia Snowe of Maine and George Voinovich of Ohio on board.

The House ended up passing a $550 billion tax cut resolution.

On Tuesday, in an economic speech, the president suggested that he would settle on the $550 billion.

"We need tax relief totaling at least $550 billion to make sure our economy grows," he said. 

But Graham and House Republicans say Grassley's late comment may have ended killing any chance that Republicans would be able to get larger cuts during the conference negotiations. Offended Republicans in the House accused Grassley of making a "secret deal" that undermined the president's tax cut agenda.

"It was a secret. I didn't know, the speaker didn't know, the whip didn't know, the committee chairman didn't know, and the president of the United States didn't know," said House Majority Leader Tom Delay of Texas.

Said to be most furious among Republicans is Vice President Dick Cheney, who appeared in the Senate on Friday expecting to cast a tie-breaking vote on a $350 billion tax cut that could be increased later in the year. Cheney was apparently broadsided with the news that Senate Republican leaders had cut a new deal making an increase all but impossible.

For many Republicans, the arrangement between Grassley and Frist amounts to the first real screw-up since Frist became majority leader. Some Republican House members are openly questioning his credibility. The White House is angry with the outcome and fear the president's tax cut is in jeopardy.

But with few Republicans willing to criticize openly their leader, much of the blame in the Senate is turning to Senate Parliamentarian Alan Frumin.

Frumin, whose job is to act as a referee on Senate activities, had been asked by GOP leaders last week to rule on a procedural move they hoped would ultimately have made the $550 billion compromise immune to a filibuster, which requires 60 votes to overcome.  Republicans say Frumin, appointed by House Minority Leader Tom Daschle, initially ruled in their favor, allowing the strategy to move forward, but then reversed course and wrote a letter to Daschle saying just the opposite. That turnaround is what forced a Republican compromise.

Several senators have expressed anger at Frumin's ruling and have called on Frist to fire him.  So far, Frist has only committed to "reviewing" Frumin's ruling.

But Graham has gone public with his complaints about Frist, and his record in the House demonstrates his experience with dogging his leaders. As a House member, Graham, who joined the Senate this year after eight years in the House, was a central figure in the coup against then-House Speaker Newt Gingrich.

For his part, those close to Frist admit that he made a mistake and "blew the play," and they acknowledge that any efforts to move ahead when lawmakers return from their Easter vacation in two weeks, could be tense.

Fox News' Carl Cameron and Julie Asher contributed to this report.