The White House may have finally figured out the secret to charming Republicans on Capitol Hill: Vice President Joseph Biden.

Biden played a critical role in crafting an agreement with Senate Republicans on tax cut extensions and has twice in two days been dispatched to the Hill to persuade Congressional Democrats to support it. And so far, he’s getting mostly positive reviews — even from some liberal Democrats angry with the details of the deal.

It appears President Barack Obama will rely on the veteran dealmaker more often in the next Congress as he seeks to work with a new reality on Capitol Hill: a Republican House majority and a strengthened Senate GOP minority. Biden served in the Senate for nearly four decades, and when Obama tapped him as his running mate in 2008, many Hill Democrats said it was the Delaware Democrat’s experience that would help the new president advance his agenda.

“He certainly is one very useful weapon that they have,” Senate Republican Conference Chairman Lamar Alexander (Tenn.) said. 

Unlike Obama’s last high-profile liaison to Congress — former Chief of Staff Rahm Emanuel — Biden has active and healthy relationships with Senate Republicans, and he enjoys a reputation as a trustworthy negotiator. It was hardly a secret that Senate Minority Leader Mitch McConnell (R-Ky.) held Emanuel in little regard, and Emanuel had perhaps even less respect among House Republicans, who saw Emanuel’s partisan nature up close when he was a member of the House Democratic leadership.

“He has excellent personal relationships. His word is good. For an administration who hasn’t spent much time trying to understand Republicans, he’s a good person to send up,” Alexander said.

Republicans said Biden’s deft negotiating abilities helped to quickly bring the tax cut talks to a satisfactory conclusion. 

And even though many Democrats are fuming about some aspects of the package Biden and McConnell crafted in secret, they acknowledge that the White House couldn’t have picked a better person to send to the table.

“I think they’ll use him a lot. He’s a good bridge,” said one Democratic Senator, who has concerns with what Biden negotiated.

“People generally like and trust him. He takes his reputation up there seriously,” added one administration official.

The administration official allowed that Obama may lean on Biden more than before in negotiations with Hill Republicans because of “the new post-midterm dynamic.” Biden was rarely called on to lobby Congress  during Obama’s first two years.

But not all the reviews of Biden are glowing. Sens. Bernie Sanders (I-Vt.) and Tom Harkin (D-Iowa) — who are vocal critics of the Biden-McConnell compromise — declined to comment Wednesday when asked whether the White House should use the vice president more often in bipartisan negotiations.

Biden got an earful from Senate Democrats during their regular Tuesday lunch this week, with many feeling the administration brokered a deal that favors tax cuts for the rich and does to little for struggling working families and the jobless.

“Biden got an unfriendly reception. Lots of hostile questioning and grousing. … Senators were not on their best behavior,” one senior Senate Democratic source said.

Part of the Democrats’ anger grew from the fact that Biden led secret back-channel discussions with McConnell, even as well-publicized bipartisan talks with Members of both the House and Senate and the administration were ongoing, the source said. Still, Democrats said Biden handled it well.

“If someone needed to sell something unpopular to the caucus, he’s the one to do it,” one Senate Democratic aide said.

And most Democrats said they don’t think Biden will bear the full brunt of Democratic anger over the package. Many liberals have long felt the president has negotiated away their priorities without receiving GOP assurances of support for other items — such as during the health care and stimulus debates — and that Obama has not called the GOP’s bluff on policy proposals over the past two years.

“I don’t think people blame Biden for any of this stuff,” another Senate Democratic aide said.

Republicans said Biden and McConnell were able to reach a compromise because they both veteran dealmakers.

“Frankly, it worked well, because it was a very candid discussion. … And the discussion had constant forward progress,” said one Senate GOP aide with knowledge of the talks.

Though they served in the Senate together for 24 years, McConnell and Biden never developed an especially close or personal relationship; they didn’t serve on the same committees or have similar interests. But over nearly a quarter-century, they developed respect for one another and share an institutional knowledge of how the process is supposed to work.

Biden is “a personal relationship politician, that’s how he operates,” the administration official said.

Not that the vice president hasn’t already been quietly helping to nurture bipartisan deals behind the scenes. During last year’s debate on the $787 billion stimulus package, Emanuel gave Biden a list of six Republican Senators to try to bring on board with the proposal. The vice president was able to deliver on three: Maine Sens. Susan Collins and Olympia Snowe and Sen. Arlen Specter (Pa.), all three of whom Biden has worked with for years.

Biden’s farewell speech to the Senate in January 2009 was almost entirely focused on the unlikely friendships he forged with numerous conservative Senators.

The Senate has “left me with the conviction that personal relationships are the one thing that unlock the true potential of this place,” he said in his speech. “Pressure groups can and are strong and important advocates. But they’re not often vehicles for compromise. A personal relationship is what allows you to go after someone hammer and tong on one issue and still find common ground on the next.”

Sen. Orrin Hatch (R-Utah), who served with Biden for 30 years, is one of the conservatives who enjoys a good working relationship with Biden. 

“They’ve had the kind of relationship where they can disagree, even strongly disagree, on policy, without being disagreeable,” a Hatch aide said. 

Though Democrats might have given a mixed review of his handling of the tax cut deal, Republicans said they would gladly welcome Biden to the negotiating table in the future.

“This is a very good model, a very productive model,” said the Senate GOP aide with knowledge of the Biden-McConnell talks. The aide added, “If [the White House] would have had this approach on at least a few items over the past two years, I think they would have had surprisingly good results.”