There’s no unanimity of opinion among Congressional Democrats about whether White House Chief of Staff Rahm Emanuel should quit his job to run for Chicago mayor. Some have said the hard-charging top aide to President Barack Obama is irreplaceable, and that without him the administration would have failed to pass core pieces of its agenda; others argue Emanuel is to blame for Obama’s failures and accuse him of giving up on too many liberal priorities too early.

But then again, House and Senate Democrats have never been of one mind about the irascible one-time House Member, who curses in nearly every sentence and rarely slows down to have a conversation.

Emanuel has not said whether he will enter the race to succeed retiring Mayor Richard M. Daley, but he has reportedly commissioned a poll to test his viability as a candidate. But many Democrats think the job could be too tempting for Emanuel resist, particularly because he once referred to it as his dream job. Democratic Reps. Luis Gutierrez, Danny Davis and Jesse Jackson Jr. also are among those Democrats mulling whether to jump into what is expected to be a crowded primary field.

“A lot of people would be happy to contribute to his mayoral race,” said a Democratic Senator, suggesting Democrats are ready for Obama to have a new top aide.

Administrations typically experience turnover after the first two years, and Emanuel — regardless of the mayoral race — was thought to be heading out soon. And some Hill Democrats, particularly those who have butted heads with Obama and his team, are ready for a few fresh faces in the White House.

Sen. Frank Lautenberg said the president should re-evaluate the roles of Emanuel and all top White House aides to begin “righting the ship.”

“This president and this administration deserves a heck of a lot more credit than it’s gotten,” said the New Jersey Democrat, who laid the blame for that lack of recognition on Obama’s staff. “In the final analysis, it has to be strained through the sieve of the team that is next to the president. So I think that it’s important to do any realigning that has to be done.”

In the House, views of Emanuel today fall along much the same lines as they did when he served as Democratic Caucus chairman and chairman of the Democratic Congressional Campaign Committee: appreciation from moderates who think he has their backs and frustration from liberals who view him as an obstacle to their goals.

[IMGCAP(1)]Congressional Progressive Caucus Co-Chairman Raúl Grijalva said he would like to see Emanuel go; he suggested the president replace him with “somebody that will work equally with all Caucus’ interests and not just work with one small faction.” The Arizona Democrat said the White House has at times ignored the wants of groups such as the CPC, the Congressional Hispanic Caucus and the Congressional Black Caucus to protect moderates.

“The caution from the White House, I think, is directly attributable to Rahm,” he said. “It’s not only the word deferential. It’s a political caution that if we hadn’t exercised it as we did, I don’t think we’d be scrambling as hard as we are in the midterms. We would have something more to show for the last two years.”

The White House should have pushed harder for a more robust stimulus bill in early 2009 and for action on comprehensive immigration reform during Obama’s first year in office, Grijalva said.

But another Democratic Senator said the president “needs somebody less partisan.”

CPC Co-Chairwoman Lynn Woolsey said a new White House chief of staff “would be refreshing.” While she was hesitant to lay the blame squarely on Emanuel, the California Democrat said that like the Democratic base, she was unhappy with the administration’s handling of major pieces of legislation, such as health care reform.

“I believe that the White House started out too close to the middle on everything and moved to the right before they needed to,” she said. “Therefore there was very little room to negotiate. … I think that weakened a lot of our legislation.”

But a Senate Democratic aide said Emanuel cannot be faulted for moving the president’s agenda to the center, given Obama campaigned on bipartisanship and promised to change the way Washington works.

“I don’t think you can blame him for being an effective strategist in carrying out the president’s plays,” the aide said.

Tensions between the White House and liberal lawmakers have simmered mostly beneath the surface; they rarely erupted into the public sphere. But in one instance last year, black lawmakers who had complained that Obama and his top aides had not paid enough attention to African-American issues staged a boycott of a committee vote on Democrats’ Wall Street reform bill, reportedly after a meeting between Emanuel and Rep. Maxine Waters (D-Calif.) failed to produce a deal.

But Financial Services Chairman Barney Frank, a liberal, said Emanuel’s help was indispensable in clearing the financial reform bill, adding that liberal criticism of Obama’s chief of staff was unfair. The Massachusetts Democrat said Member discontent is probably more about their frustration with Obama for not accomplishing things that were politically unattainable.

“Some of my colleagues are unhappy with the president to some extent because he doesn’t have a magic wand,” he said.

In further evidence that frustration among liberal lawmakers is far from universal, Rep. Jan Schakowsky, a fellow Illinois Democrat, described Emanuel as an “invaluable asset” to the president and to House Democrats. She said “the Obama agenda of successes adds up to a very substantial gain for progressives” and that Emanuel played a key role.

Sen. Charles Schumer (N.Y.), the Senate’s No. 3 Democrat, said Emanuel “has done an excellent job of implementing the president’s agenda and deserves a lot of credit for it.”

One senior Senate Democratic aide said liberals’ discontent with Emanuel is not surprising, given they “see him as too willing to negotiate and to cut deals.” But the aide said the Senate Democratic leadership, and Majority Leader Harry Reid in particular, have found Emanuel to be reliable, accessible and not afraid to make a decision.

The Nevadan has found Emanuel to be an asset to the president for the same reasons many moderates have.

“He wants to get things done. He’s very smart and he’s got a good political head,” Sen. Joe Lieberman (ID-Conn.) said.

Emanuel also has particularly close ties to sophomore House Democrats who he helped elect during his tour at the DCCC in the 2006 cycle, when Democrats won control of the chamber. Many of those Members are moderates from GOP-leaning districts, and one of them said he suspected Democrats would in better shape this cycle had more of Emanuel’s advice had been heeded.

“Things like taking cap-and-trade before health care when we didn’t have the votes in the Senate — those are, I think, political mistakes,” the lawmaker said. “Those are the kind of mistakes Rahm wouldn’t make.”

Freshman Rep. Jared Polis (D-Colo.) said that if Emanuel were to leave the White House, he hoped Obama would replace him with someone who is equally familiar with Capitol Hill. Emanuel served in the House for six years before heading to the West Wing. He also served as a top adviser to President Bill Clinton.

“I hope that somewhere in the mix there is either a current or former Member of Congress who is held in high esteem that can continue a close relationship with the House Caucus,” Polis said.

Rep. Robert Andrews (D-N.J.) recounted Emanuel’s hands-on approach to locking down votes for the final House health care vote in March, noting that Emanuel intermittently stepped out of his son’s bar mitzvah to take calls from waffling Democrats.

Andrews said he had encouraged Emanuel not to leave the administration, adding that he would leave a hole that would be difficult to fill.

“You have to be in an institution to really understand its rhythms, and he understands ours,” Andrews said.

The White House declined to comment for this story but asked several friendly lawmakers to call Roll Call with their thoughts on his tenure.

Rep. Charlie Rangel (D-N.Y.) said late last week that he would prefer Emanuel over an untested replacement. “I know what I got. So I am satisfied with that, and I don’t know what might replace it.”