After weeks of bitter partisan bickering, Congress today approved a two-month extension of a payroll tax holiday, unemployment benefits and the Medicare “doc fix,” setting up another round of debate that could begin as soon as next week.

The Senate went first this morning, passing a measure by unanimous consent that would deem the package of extenders as passed when the chamber received the legislation from the House. It also appointed conferees to a conference committee that has been tasked with hammering out a full-year extension. The House passed its measure shortly after by unanimous consent, effectively sending it to President Barack Obama for his signature.

Freshman Rep. Rob Woodall (R-Ga.) was originally scheduled to preside over the chamber for today’s session, he said, but Speaker John Boehner (R-Ohio) decided he would do it himself.

Boehner declined to answer questions exiting the chamber. But as a crush of reporters followed him into Statuary Hall, Rep. Steve Cohen (D-Tenn.), there for a Democratic news conference, reached out his hand to Boehner and said, “You’re a good man. I feel for you.”

Many House Republican freshmen expressed deep reservations about the deal, some of whom even threatened to catch planes back to Washington to object to today’s unanimous consent agreement. They eventually backed down, allowing the deal to pass.

“I saw tears in his eyes. I saw a man who has deep feelings for human beings and this institution and was alone today,” Cohen said of Boehner.

House Democrats largely declined to twist the knife into their Republican colleagues at their news conference, heralding a victory only for the “American people.”

House Minority Whip Steny Hoyer (D-Md.) declined to answer questions about the Democrats’ stance heading into negotiations for the full-year payroll tax cut extension.

Rep. John Dingell (D-Mich.), the dean of the House, said he was “hoping this is a sign of good things to come” and that he hopes rank-and-file Republicans “will learn to follow their leader,” Boehner.

Unlike his House colleagues, Senate Majority Leader Harry Reid (D-Nev.) did get into some of the specifics of the negotiations ahead. He said after clearing the package by unanimous consent that he expects conferees to start negotiations on a full-year extension in the week after Christmas.

“Everything we do around here does not have to wind up in a fight,” Reid said. “This is a new day,” he continued, before noting that “everything is on the table” in the second round of negotiations. He pointed out that Democrats could revisit the millionaire surtax, which they pulled off the table in brokering the short-term deal, as a potential offset for a one-year extension.

“I’ve talked to Senate Republicans, plural, who think that there should be a fair tax on rich people,” Reid said.

Earlier this month, Republican Susan Collins (Maine) introduced a bill with Sen. Claire McCaskill (D-Mo.) that would levy a surtax on millionaires with a carve-out for small-business owners.

Though the fight over the more modest bill ended anticlimactically, with both the House and Senate approving it without objections, there is no guarantee this second round of talks will be any easier than the first. Last week, leaders had not been able to agree on how to pay for the full-year package, which came with a price tag of about $190 billion. The nearly $40 billion two-month extension is largely paid for by increasing fees on mortgages refinanced through Fannie Mae and Freddie Mac.

Moreover, many of the named conferees for the formal talks were members of the Joint Committee on Deficit Reduction, which also failed as a result of arguments over how to reduce the budget and whether to raise taxes.

Reid announced his appointments to the conference committee in a news conference after Senate action on the bill: Sens. Max Baucus (Mont.), a member of the super committee, Benjamin Cardin (Md.), Bob Casey (Pa.) and Jack Reed (R.I.).

Boehner, who announced his conferees earlier this week, included super committee veterans Fred Upton and Dave Camp of Michigan. House Minority Leader Nancy Pelosi (D-Calif.) selected Reps. Chris Van Hollen (Md.) and Xavier Becerra (Calif.), also super committee veterans, as two of her five negotiators.

Reid said he was “very disappointed” in the conferees selected by Boehner because several of them had stated objections to extending the payroll tax holiday at all.

The most complicating factor for the success of the talks, however, is not the composition of the group, but the environment in which it must work. As the 2012 elections draw nearer, and leaders worry about their vulnerable Members, agreement will be more difficult to reach. And Congress will have to take care of many other issues, from averting a Federal Aviation Administration shutdown at the end of January to potentially negotiating the Bush-era tax cuts in a lame-duck session.

For now, though, leaders seem relieved just to go home for the holidays and give credit to their colleagues across the aisle. Reid especially thanked Senate Minority Leader Mitch McConnell (R-Ky.), whose statement Thursday in favor of a short-term deal pressured House Republicans to approve it.

“Sen. McConnell did what I thought was right for the country,” Reid said.