WASHINGTON, D.C. — Just after 5 p.m. Thursday, the headcount in the Senate shifted one seat to the Republican side, as Sen. Scott Brown (R) of Massachusetts was sworn in as the 41st Republican. But well before his arrival in Washington, leaders on both sides of the aisle have been recalibrating strategies for party agendas that take into account the new clout of the minority.

 Majority Democrats no longer hold the 60 seats needed to break a filibuster. That means they will have to reach out to at least one Republican to move major legislation. Some centrists in Democratic ranks say that’s all to the good.

 "I hope it means that Democrats and Republicans will be working to find common ground. Now that we need to, I hope we do more of it,” says Sen. Blanche Lincoln (D) of Arkansas.

Republican leadership is going back to the demands they made at the beginning of the 111th Congress, before Sen. Arlen Specter (D) of Pennsylvania quit GOP ranks to caucus with Democrats.

With Senator Specter’s exit, Republicans lost much of their bargaining power. With Senator Brown’s arrival, they get it back. Republicans want their ideas to be incorporated in major legislation moving forward.

 “What we said at the beginning of the 111th Congress is that Democrats are not going to get away with filing procedural motions that don’t have Republican input,” says Don Stewart, a spokesman for Republican Senate leader Mitch McConnell. “Theoretically, what Brown’s arrival means is that they have to negotiate with us,” he adds.

Brown consistently tells reporters that he doesn’t see himself as the 41st Republican, but that his arrival means that all Republicans have a shot at contributing ideas to the legislative process. Asked today what his own priorities are, he said: “Well, obviously it’s jobs, jobs, jobs, jobs. Try to figure out how we can get the economy moving again.”

At a briefing on a new jobs agenda Thursday, Sen. Charles Schumer (D) of New York said that Democrats had learned from the Massachusetts defeat.

“I think we can say to the people of America: We heard the message of Massachusetts, and it didn’t mean 'don’t do health care',” he said. “Theysaid: focus immediately and don’t take your focus off jobs.” Some Democrats note that it’s not clear that Brown will always vote with Republicans. “We’ll have to see if Mr. Brown just wants to march in lock step or be more independent,” says Sen. Tom Harkin (D) of Iowa. “If I looked like him [Senator Brown], I’d be president of the United States today," quipped Sen. John McCain (R) of Arizona, one of the GOP’s most independent voices.

Brown calls Senator McCain his mentor in the Senate. He told Massachusetts voters that he would be an independent voice in the Senate.