A far cry from the underdog days, congressional Republicans are now enjoying their time in the political sun — with greater majorities in the House and Senate, a popular second-term Republican in the White House and what they call a mandate from American voters to pursue their agenda with zeal.

“I think the American people gave Republicans a mandate to move forward with an agenda and that’s what we will do,” said one Senate conference aide.

As for those Democratic senators who, she said, obstructed everything from judicial confirmations to the energy bill and tort reform in the last Congress, “perhaps they are going to have to realize that they will have to move a little bit to the center and compromise with the Republican agenda. Because if they want to stay in office they won’t be able to block the will of the popular majority the people have supported.”

Republicans won the House in 1994 after 40 years of Democratic domination and never looked back. They have maintained their majority since then, and as of this year’s election, have a 231-201-1 margin, with two seats still to be decided next month during run-off elections in Louisiana.

The GOP took over the Senate in 1994, lost the majority by one vote when independent Sen. Jim Jeffords switched parties in 2001, and won it back in the 2002 congressional election. In last week's election, the Republicans gained seats, increasing their majority to 55 with 44 Democrats and Jeffords voting with the minority party.

With a second loss to President Bush (search), Democrats now find themselves in a weakened state legislatively. To make matters worse, Senate Minority Leader Tom Daschle was defeated by conservative Republican John Thune.

Will Marshall, president of the Progressive Policy Institute (search), the think tank of the centrist Democratic Leadership Council, said he fears that the Republicans will use their strengthened hand to continue to bully and repress Democratic proposals and positions in Congress.

“Now their numbers are larger and the newer members are really tied to the right,” Marshall said, referring to new senators like Tom Coburn of Oklahoma, who supports the death penalty for doctors who perform abortions, and Jim DeMint of South Carolina, who said homosexuals should not be teaching in public schools.

“Republicans have abused their power, they have stifled the minority,” he said, pointing to the House where procedural decisions are often decided by Republicans during a weighted committee process. “The Rules Committee has become an engine of suppression.”

House Minority Whip Steny Hoyer (search) has long complained that the Republican leadership has used the Rules Committee to prevent Democratic legislation from ever reaching the light of day. He called their tactics unprecedented.

“Something that the polls show but the pundits aren’t talking about is the desire in this country for bipartisanship,” Hoyer, of Maryland, told FOXNews.com after the election. “I think that my Republican colleagues in Congress would do well to heed this desire for change in how business is done in Washington.”

But Republicans say it is time for the Democrats to take a little of their own medicine.

“A lot of those complaints are accurate,” said Mike Franc of the Heritage Foundation. “[Republicans] learned by example from the previous Democratic majorities. When you have a narrower majority — the way the Republicans have their majority — the more imperative it is to use every tool you have in your toolbox.”

Capitol Hill sources said the recent election will allow the president’s policy goals to move forward. Among those priorities are Social Security (search) reform, tax code and tort reform and an overhaul of national intelligence.

As for social policy, which tends to divide Capitol Hill the most, Bush senior political adviser Karl Rove told "FOX News Sunday" that he expects a constitutional amendment banning gay marriage (search) to move forward. Looming Supreme Court nominations also promise to feature prominently on the Republican agenda.

“This solid victory by President Bush and the additional senators and House members has changed the calculus,” said Larry Sabato, director of the Center for Politics (search) at the University of Virginia. He said the president and Congress will likely work fast, before the 2006 midterm election campaigning kicks in.

“I bet you we are in for a very productive period in Congress,” he said.

Others warn that not all GOP senators are conservative, and moderate members will continue to hold their colleagues back when it comes to big tax cuts and social reforms. Opposition to any Republican bills in the form of Democratic filibusters (search) will still require 60 votes to override.

But, said John Samples, director of the Center for Representative Government at the Cato Institute (search), conservative Democrats will no doubt team up with the growing conservative base in the Senate to get bills finished.

“[Moderates] are no longer as necessary; they will be in a more weakened position,” Samples said.

One such moderate has already faced the wrath of conservatives.

After a remark that he later said was misconstrued to suggest he would not allow hearings for anti-abortion judges, Pennsylvania Republican Sen. Arlen Specter, a moderate just elected to a fifth term, found that his ascension to the top of the Judiciary Committee is now in question. Conservative groups have already lined up to thwart his chairmanship, saying he would be obstructing the will of the voters.

Sarah Chamberlain Resnick, executive director of the Mainstreet Partnership (search), a coalition of moderate Republican members, said she is not worried that Specter's future is in doubt.

"We have great confidence that he will become the next committee chairman," she said, adding that other issues of concern to moderates, including stem cell research (search), will be pursued despite conservative opposition. "I'm hoping this is one area that we can unite behind on."

Resnick disagreed with Sample about the decreasing role of moderates, saying they too gained ground this year and helped to re-elect Bush by wider margins.

"[Conservatives] have gotten a victory, which is great, but they fail to mention that the moderates were fundamental in handing that victory to the president," she said, pointing to increases in support for Bush among Hispanics and women.

Meanwhile, House Democrats appear to be in the worst situation, said John Fortier of the American Enterprise Institute (search). “In the House, you don’t need the minority — the rules allow the majority to get things done without them," he added. “For them, it’s not a happy time.”