House Speaker John Boehner of Ohio heads to a meeting on Capitol Hill Wednesday. He repeatedly declined to say Wednesday whether the House would take up the Senate’s so-called “clean” bill. (Susan Walsh/AP)

Congressional Republicans have been plagued in recent years by a fractious and politically harmful family feud. Wednesday provided fresh evidence that the party’s sweeping November midterm wins have done little to alter that dynamic.

House and Senate Republicans remained sharply at odds over how to fund the Department of Homeland Security while continuing to do battle with President Obama over immigration. With just two days left before funding authority for DHS runs out, there was great uncertainty about whether and how lawmakers can get a bill to Obama’s desk in time to avoid a partial shuttering of the department.

The Senate on Wednesday advanced a measure that would fund the agency through September and forestall any kind of shutdown. But that proposal, crafted by Senate Majority Leader Mitch McConnell (R-Ky.), could face stiff GOP resistance in the House, where Speaker John A. Boehner ­(R-Ohio) has not been willing to say whether he would bring the bill to a vote.

The debate has inflamed tensions between House and Senate Republican leaders, who are struggling to govern in the early days of their unified congressional majority. Rank-and-file GOP members have also lobbed barbs at the other chamber.

On a 98-to-2 vote, the Senate’s DHS bill cleared a key procedural hurdle that could set up a final vote as soon as Thursday. It would fund DHS through the end of the fiscal year, and it would not affect Obama’s executive actions on immigration.

Congress must pass legislation by February 27 to keep the Department of Homeland Security running. The agency faces a partial shutdown if its budget doesn’t get Congress’s and the president's approval. Here's a breakdown of what’s at stake. (Pamela Kirkland/The Washington Post)

But Boehner repeatedly declined to say Wednesday whether he would take up the Senate’s “clean” bill. He pointed out that the House has already passed its own measure, which would fund DHS but block money for Obama’s immigration actions. Senate Democrats have prevented that bill from advancing four times.

“Until the Senate does something, we’re in a wait-and-see mode,” Boehner told reporters after leaving a meeting with rank-and-file Republicans.

At the meeting, according to members in attendance, Boehner revealed that he had not spoken to McConnell in two weeks. McConnell’s office said it was much ado about nothing, simply a result of last week’s recess interrupting their normal weekly meeting, which resumed Wednesday.

Frustration among rank-and-file Republicans also flared up, with House conservatives expressing disappointment with McConnell’s decision to take up the “clean” bill Democrats demanded.

“Right now, Harry Reid’s still running the Senate. That’s a sad day,” said Rep. Matt Salmon (R-Ariz.), who argued that a “clean” DHS bill could not pass the House with a majority of Republicans’ support.

Sen. Mark Kirk (Ill.), a moderate Republican, defended McConnell and laid blame at the feet of House Republicans.

“Mitch has been around the block a few times [and we] will be able to extract ourselves from a totally unnecessary battle that the House has put us in,” Kirk said.

Asked about the possibility of a shutdown of the Department of Homeland Security during a news conference on Wednesday, Speaker of the House John Boehner repeatedly urged the Senate to act on the issue. (AP)

Democrats were happy to twist the knife.

“There’s trouble in paradise. I don’t understand it,” said a chuckling Sen. Richard J. Durbin (Ill.), the second-ranking Senate Democrat.

At a town-hall-style forum in Miami hosted by MSNBC and Telemundo, Obama promised that Republican resistance would not nullify his immigration actions.

“If Mr. McConnell, the leader of the Senate, and the speaker of the House, John Boehner, want to have a vote over whether what I’m doing is legal or not, they can have that vote,” he said. “I will veto that vote because I’m absolutely confident it’s the right thing we do.”

McConnell has devised a plan to fund DHS and allow conservatives to vent their frustration with Obama separately. He intends to hold a vote on a standalone measure that would undo Obama’s 2014 actions, including stemming of deportations for millions of undocumented immigrants.

But the bill faces a difficult path until DHS is actually funded beyond midnight Friday. Reid said he would encourage his caucus to block the bill until both chambers of Congress pass a DHS spending bill and send it to the president.

In a partial DHS shutdown, nonessential workers would be furloughed until the department’s funds are replenished.

DHS Secretary Jeh Johnson won support from two of his Republican predecessors — Tom Ridge and Michael Chertoff — who joined him Wednesday in warning that a shutdown would hurt the department’s ability to protect the country.

Ridge, the department’s first secretary, under President George W. Bush, acknowledged that he strongly opposed Obama’s executive orders on immigration.

But he called it “wrong and folly” to express that opposition by refusing to fully fund DHS, which he likened to not funding U.S. soldiers.

“These are soldiers at DHS,” he said. “They wear a different uniform, but the goal and objective and mission is the same — keeping America as safe as possible.’’

If Boehner does not take up the Senate bill, which Democrats believe could win House passage with their support and a minority of Republicans, there would be little time to formulate an alternative plan.

One option is a continuing resolution that would keep DHS funded for a short period and would allow the two chambers to continue debating, perhaps in a House-Senate conference.

At the White House, Obama met with 17 immigration advocates before he traveled to Miami. At the town hall event there, he defended his actions on immigration, which have run into resistance from a federal judge. Obama vowed a vigorous fight against the judge’s recent ruling.

“We’re going to be as aggressive as we can,” Obama said. “In the meantime, what we said to Republicans is, ‘Instead of trying to hold hostage funding for the Department of Homeland Security, which is so important for our national security, fund that and let’s get on with passing comprehensive immigration reform.’ ”

Senate leaders are working to expedite their bill to give the House as much time as possible to address it. So far, it’s run into little resistance in the chamber.

Sen. Ted Cruz (R-Tex.), who led the 2013 effort to defund the federal health-care law that many blamed for a government shutdown that year, showed no signs Wednesday that he was preparing to wage a similar fight to slow progress of the Senate’s DHS bill.

“Nothing is to be gained by a delay of 12 hours or 24 hours or 36 hours,” Cruz said.

But even as the 2013 shutdown remained fresh in the minds of many Republicans who were fearful about a new round ­of blowback if DHS is forced to retrench, some conservatives showed no fear, illustrating the cavernous divide over political strategy that persists in the GOP.

Rep. Steve King (R-Iowa), an outspoken opponent of Obama’s immigration actions, cast the last shutdown’s impact on DHS as a minor event.

“I don’t remember anybody noticing,” he said.

“I don’t remember anyone complaining.”

Jerry Markon, David Nakamura, Mike DeBonis and Katie Zezima contributed to this report.