White House officials say it’s the same role the vice president, who served nearly four decades in the Senate, has played since the start of the administration. But in the absence of Emanuel, who formerly served as Obama’s chief of staff and as a House member, no one in the West Wing matches Biden when it comes to his ties on the Hill, depth of knowledge on how Congress works and having the members’ trust on both sides of the aisle.

Obama gave Biden a pivotal role in the tax-cut talks on the Hill, making him the lead negotiator with Senate Minority Leader Mitch McConnell (R-Ky.). Biden is also the point person on the White House’s efforts to win enough Senate votes for a new START treaty during the lame-duck session. And he met last week at the White House with Rep. Darrell Issa (R-Calif.), who is preparing to take over as chairman of the Oversight and Government Reform Committee and who is expected to dig into the administration’s spending of economic stimulus money.

But his most public assignment of late has been as the White House’s emissary to Democrats, tasked with trying to tamp down their anger over a tax-cut deal hammered out largely between the White House and GOP leaders.

The vice president had a blunt message for House Democrats on Wednesday during a closed-door session, according to members who attended. “It’s as good as it gets,” Biden told them, taking a hard line that did not go well with everyone.

“The vice president said, ‘This is the deal, take it or leave it,’” said Rep. Henry Waxman (D-Calif.).

But at least one member felt Biden’s attentiveness was a salve for Democrats wounded by the product and the process that cut them out. “He made it easier,” said one attendee. “The vice president was pitch-perfect in tone. He was respectful. He really talked to the members in a way that they knew he was listening.”

Asked whether he had picked up any support as he left the meeting, Biden responded: “Oh yeah, we got a couple of ’em.”

During his appearance before the Senate Democratic Caucus on Tuesday, Biden began by lecturing some of the more liberal of his former colleagues over the political need for the deal — only to be cut off by Sen. Patrick Leahy (D-Vt.), who told him “to relax.”

“It got a little contentious,” said a Senate Democrat who attended the meeting. “He started off by saying, ‘You liberals may [oppose] this, but we’ve got to do it. Then [Leahy] told him to relax; it’s not doing you or us any good.”

Biden made a point to remind many of those in the room that he had campaigned for them this year.

McConnell said the White House has stepped up its contact with him and other Republicans since the GOP’s decisive electoral victory on Nov. 2. And with the power of congressional Democrats diminished, the vice president’s portfolio has been expanded to include more direct talks with McConnell and other GOP leaders.

“He’s been heavily involved up here in talking to a variety of different people,” said McConnell, who added that Biden “played a very important and constructive role” in the negotiations over the tax-cut package.

“Those talks made this whole deal possible, the two of them negotiating and transacting,” said a senior Senate GOP aide of the Biden-McConnell discussions.

In addition to the tax-cut talks, Biden and McConnell had a one-on-one meeting recently on moving forward on the new START treaty, a major priority for the White House, according to Senate aides. Debate over that nuclear arms accord with Russia is expected to begin after the Senate completes work on the tax package.

“I think the main point I would make is that there’s been a lot more conversations, not just with me but with Republicans in general over the last couple weeks. More than over the last couple years,” McConnell said in describing White House outreach to GOP congressional leaders since the Democrats’ Election Day debacle. “I say that as a compliment. I think the voters clearly sent a message that they wanted us to do things together, and I think the early indications are that that may be possible.”

For the first two years of the administration, Emanuel was a regular on the Hill for big legislative fights, conducting personal negotiations over the economic stimulus package and health care law, among other issues, and calming Democratic nerves on key pieces of Obama’s agenda.

Emanuel’s skills as a partisan broker fit well in a Democratic-controlled Congress, where he could try to pick off a Republican senator here and there but ultimately could go it alone. In contrast, Biden has long, sometimes close relationships with Republicans, which will be crucial in the coming months.

For instance, Biden and Indiana Sen. Richard Lugar, top Republican on the Senate Foreign Relations Committee, worked together extensively on legislation over the years on such topics as climate change, foreign aid, violence against women and U.S.-Pakistan relations.

Biden, who clashed repeatedly with Minority Leader John Boehner of Ohio, the speaker-designate, over the past two years, has also been trying to soften his image with House Republicans. After meeting with Issa, the two men issued a joint press release, saying they had “identified some areas of agreement, including the need to enforce full compliance with reporting by recipients of recovery act funds and to have follow-up conversations about other areas where they can work together.”

Issa also noted that he knew Biden “before he was vice president, and we should’ve been working together” previous to this meeting.

Biden and Issa’s aides plan to meet again before the end of the year to follow up on what their bosses started, according to one GOP insider.

With many Democrats furious over the tax-cuts deal — both on the merits and for what they see as a White House runaround of the bipartisan group of members and administration officials tapped to negotiate a compromise — the White House has been trying to downplay Biden’s role in the tax-cuts deal, even rejecting the notion that he was doing the negotiating.

The vice president’s “role at the outset of this was not as a negotiator,” said White House senior adviser David Axelrod. “His role was as someone who had relationships across the aisle in the Senate as a result of 36 years in the United States Senate. And in his soundings, he got a sense of what was possible and what was not possible. And he became more actively involved at the end in negotiations as things accelerated because of that relationship.”

“One of the great values he has here is his knowledge of the Senate: the personalities there, years of relationships,” Axelrod added. “And we’d be crazy not to take advantage of that.”

A senior administration official described Biden’s discussions with McConnell as “sidebar conversations that were very much a part of the main negotiations” but disputed the idea that Biden is filling Emanuel’s former role.

“It’s a continuation of a role that ebbs and flows,” the official said.

Carrie Budoff Brown and Jonathan Allen contributed to this report.