President Obama on Thursday implored Republican lawmakers to pass a stalled, immigration-reform package, but the message quickly faded away as GOP leaders kept a laser-like focus on the botched rollout of the federal website for Obamacare’s new health exchanges.

Obama and his surrogates had hoped that in the wake of the recent government shutdown, they could pressure Republicans —weakened by the funding fight — to take up immigration reform, one of the president’s key second-term priorities.

But as Obama on Thursday championed a fix to the nation’s broken immigration system, Republicans on Capitol Hill were busy grilling contractors who built the glitch-plagued Obamacare website.

It’s an issue the White House won’t soon shake: Obamacare, for better or worse, will be the dominant conversation in Washington in coming weeks and months.

And the president acknowledged he had precious little time to get immigration reform done before 2014’s midterm elections.

“It doesn’t get easier to just put it off,” Obama said from the White House. “Let’s do it now. Let’s not delay. Let’s get this done, and let’s do it in a bipartisan fashion.”

White House chief of staff Denis McDonough also met with business leaders on Thursday to push immigration reform.

For their part, Republicans reacted to the president’s latest immigration speech with a collective shrug.

“I can tell you how much it moved the needle,” one senior House GOP aide told the Washington Examiner. “Not at all.

“The president can try to dictate terms all he wants but we have absolutely zero reason to rush on this,” the aide added. “Obviously, Obamacare will be the main focus in the short term.”

The problem for the White House is not just that Obamacare is distracting from the immigration message but that Republican leaders are drawing parallels between the Senate-passed bill and the president’s health blueprint.

“The House will not consider any massive, Obamacare-style legislation that no one understands,” said Brendan Buck, a spokesman for Speaker John Boehner, R-Ohio.

The White House was well aware of efforts to link Obamacare to immigration reform, with officials Thursday actively trying to separate the two policies.

“There’s no connection between the Affordable Care Act and comprehensive immigration reform,” White House press secretary Jay Carney insisted.

Carney on Wednesday also insisted that the controversy over Obamacare would not distract from Obama’s efforts to secure an immigration bill, saying the president “firmly” believed he could have legislation on his desk by the end of the year.

But the White House push for a “comprehensive” plan faces an uphill climb in the GOP-controlled House.

A handful of GOP lawmakers are floating piecemeal plans that focus primarily on border security and have more rigid citizenship standards for immigrants living in the U.S. illegally.

House Judiciary Chairman Bob Goodlatte, R-Va., has also said he will move immigration legislation piecemeal as opposed to a single bill as in the Senate.

Conservatives, still licking their wounds from the shutdown clash, are hardly eager to give the president a signature political win.

After a dismal showing among Hispanic voters in the 2012 presidential election, GOP congressional leaders vowed to make their party more appealing to Latinos. Immigration reform, they say, is a key step to convincing Hispanic voters the Republican Party is in tune with the issues they most care about.

Considering that political predicament, some immigration-reform advocates said Republicans would be foolish to sweep aside immigration reform in an effort to keep Obamacare in the limelight.

“It would be sheer lunacy to believe that given everything that’s happened, they can now spend the rest of the year solely trying to destroy a program they’ve failed to destroy during the last three years,” said Simon Rosenberg, a campaign adviser for former President Bill Clinton and founder of the think-tank, NDN. “They have to do something positive given where their poll numbers are.”

Republicans absorbed most of the blame for the impasse over federal funding and raising the debt ceiling, polls show. Party leaders are hoping to recast the nation’s attention on the flawed Obamacare launch rather than the GOP’s unsuccessful push to defund the law.

The Senate immigration bill passed in June has been dead on arrival in the House. And some immigration-reform supporters contend Obama is to blame for the lack of progress, saying he should spearhead talks — even amid the Obamacare drama — with Republicans rather than insist they rubberstamp the Senate bill.

“He’s more concerned with using this issue for political purposes and regaining the House than trying to help Latinos,” said Alfonso Aguilar, executive director of the Latino Partnership for Conservative Principles. “It's hypocritical.”