WASHINGTON — The ranks of the moderate Republicans in Congress have been decimated in recent elections, and those who remain in politics have been marginalized by their own party, which has veered sharply to the right over the past generation.

But now this beleaguered minority has an opportunity to wield outsized influence on what President-elect Barack Obama can accomplish in Congress.

Although Democrats made big congressional gains in the 2008 election, they remain a vote or two short of a 60-vote majority they need in the Senate to keep a tight rein on GOP filibusters that can gum up the works.

The support of just one or two moderate Republicans could be decisive in a close, party-line vote on issues such as union rights and economic rescue plans. So while there may be fewer moderates in Congress, they are in for a lot of attention.

“The power of moderates is declining in the country: They are fewer in number, and the country has polarized,” said Thomas Schaller, a political scientist at the University of Maryland, Baltimore County. “But … there are always going to be people in the middle who have decisive power.”

Vice-President Elect Joe Biden and Obama’s incoming budget director, Peter Orszag, already have met with Sen. Susan Collins, R-Maine, about economic stimulus legislation. Obama’s team has consulted Rep. Mike Castle, R-Del., an expert on education, about school issues. Obama’s choice for secretary of transportation, Ray LaHood of Illinois, was a moderate GOP leader in the House of Representatives until he retired this year.

But if recent elections are any guide, being a moderate — one who supports abortion rights, for example, opposed the war in Iraq or supported labor unions — is hazardous to a Republican’s political health. Many swing voters have been alienated by President George Bush’s policies and perceptions that the Republican Party is dominated by extremists.

Republican lawmakers defeated recently include such centrists as Rep. Christopher Shays, R-Conn., and Sen. Gordon Smith, R-Ore. Retirees included moderates Sen. John Warner, R-Va., and Rep. Jim Walsh, R-N.Y.

In the House, where rules provide for strict majority rule, Democrats will have little need to court Republicans to pass most of their agenda. But in the Senate, a minority of 41 can filibuster to prevent a bill from coming to a vote. Senate Democrats probably will wind up with 58 or 59 members, depending on the outcome of a disputed Senate election in Minnesota.

Moderate Republicans worry that members of the conservative wing are not going to change their ways in response to their party’s election drubbing.

“I would hope that the more conservative members of our caucus would take a look at these election results,” Collins said. “It’s difficult to make the argument that our candidates lost because they were not conservative enough.”

It remains to be seen how aggressively Republicans will try to wield the filibuster threat. They have signaled that they will fight Obama’s economic recovery plan if it moves too quickly, but there are political risks if the GOP is seen as obstructionist at a time when voters are clamoring for relief.

One issue in which Republicans are spoiling for a fight is on legislation to make it easier for unions to organize workers. If Democrats are going to pass the bill in the Senate, they might well need Sen. Arlen Specter, R-Pa. — the only Republican who voted to bring the bill to a vote the last time it came up.

But the issue puts Specter in a position that is typically challenging for Republican moderates. He faces re-election in 2010, in a state with a strong union presence and an electorate that has recently voted more Democratic. That puts pressure on him to support the labor bill. But Specter often faces opposition from fellow Republicans for being too liberal: In 2004, he faced a primary fight from the right from Pat Toomey, who is president of the Club for Growth, a conservative, anti-tax group.

Toomey predicts that if Specter casts a decisive vote on the labor bill, “he virtually assures he will deal with a primary challenge and he hands the challenger a powerful issue.”

Specter said in a recent interview with The Morning Call in Allentown, Pa., that the situation assures that moderates will be at the center of controversy. “There are only a few of us moderates — we could fit in a phone booth,” he said. “To make that 60th vote, it may be that we’ll be in big demand.”