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These changes have the potential to reduce the importance of Republican moderates, especially in the Senate, and embolden conservatives in the White House and elsewhere, these analysts said. But they also might heap unrealistic expectations on Senate Majority Leader Bill Frist (R-Tenn.), who still lacks a filibuster-proof majority as he weighs a 2008 presidential bid.

The GOP's bare Senate majority of 51 members will grow to 55, but the impact goes beyond mere numbers.

Replacing Sen. Ernest F. Hollings (D-S.C.), often a bridge between the two parties on spending and deficit questions, is Rep. Jim DeMint, whose call for abolishing federal income, payroll and estate taxes is considered extreme even by some fellow Republicans. Succeeding Sen. John Breaux (D-La.), a key broker on sticky issues such as Medicare, is mainstream Republican Rep. David Vitter, who seems unlikely to play such a bipartisan role.

"Regrettably, we have seen an erosion in the Senate of centrists on both sides of the aisle," said Sen. Olympia J. Snowe of Maine, a Republican moderate whose leverage may drop substantially in the next Congress. She said she hoped Bush will push for cooperation between the two parties.

Another GOP moderate, Sen. Lincoln D. Chafee (R.I.), expressed even deeper disappointment, telling the Providence Journal he would not rule out switching to the Democratic Party.

While Frist celebrated the victories that will leave only four Democratic senators in the former Confederacy, some political scholars noted he must oversee a diverse delegation that still has enough moderates to occasionally frustrate Bush's agenda. But in light of Tuesday's election results, conservatives in the House and White House may show less patience with roadblocks to drilling for oil in Alaska wildlife refuges or limiting civil liabilities for doctors and others.

"The locus of power has moved dramatically to the right in the Senate," said Marshall Wittmann, a senior fellow at the Democratic Leadership Council and former staff member for the Christian Coalition and Sen. John McCain (R-Ariz.). Whereas Democratic and moderate Republican senators often could derail or temper conservative initiatives from the House, he said, "that now becomes much more difficult."

The trick for Frist, he said, will be to nudge Congress's agenda to the right without appearing to cede control to hard-core partisans such as House Majority Leader Tom DeLay (R-Tex.). With a beefed-up majority that still lacks the 60 votes needed to block a filibuster, Wittmann said, "Frist has a dilemma that he may luxuriate in or he may rue."

His best option, several analysts said, may involve appealing to Democrats who will view Tuesday's results as a warning to those who try to thwart the president's agenda.

Frist's GOP colleagues already are raising expectations. Sen. George Allen (R-Va.), head of the National Republican Senatorial Committee, told reporters that voters should expect a "reinvigorated, stronger Republican majority in the Senate" that will push aggressively for new judicial appointments and an array of measures the Democrats have stymied in recent years, such as a far-reaching energy bill.

According to Allen, Americans said, "We don't want partisan bickering, we want action."

But Frist's challenge is greater than many people realize, said James Thurber, director of American University's Center for Congressional and Presidential Studies. The election results, he said, will embolden DeLay and other House leaders to accelerate their strategy of "sending fairly conservative and edgy legislation to the Senate." Awaiting it there will be staunch conservative newcomers such as DeMint and senator-elect Tom Coburn (R-Okla.), considered the most right-leaning of the nine new senators elected Tuesday.