WASHINGTON — Less than six weeks in his powerful perch on Capitol Hill, Senate Majority Leader Mitch McConnell, R-Ky., is on the verge of watching one of his most important promises – to never again shut down the government – go up in smoke.

Lawmakers on Friday began a 10-day hiatus, leaving them just four days when they return to pass funding for the Department of Homeland Security to avoid the shutdown of a key federal agency. The DHS budget fight follows an effort among GOP conservatives to roll back President Obama’s recent executive orders on immigration.

Conservatives are adamant that the security agency should be funded only if the legislation also overrules Obama’s orders, which prevent the deportation of millions of illegal immigrants. But Senate Democrats, even the few who oppose Obama’s moves, have blocked the House-passed legislation with repeated filibusters.

That has left McConnell trapped inside a legislative box that he had vowed to avoid – and one that for the previous four years his close ally, House Speaker John Boehner, R-Ohio, frequently wandered into without an exit strategy.

McConnell was determined not to repeat those mistakes.

“Let me make it clear: There will be no government shutdowns,” McConnell said the day after he won reelection and a Republican rout gave his party the Senate majority.

But this week, McConnell declared the Senate stuck, and in need of Boehner’s help. The speaker was not in a helping mood. Boehner said he has no interest in passing legislation through the House that could draw Democratic support in the Senate. “The House has done its job,” Boehner told reporters Thursday. “We’ve spoken. And now it’s up to the Senate to do their job.”

A shutdown of one agency would not cause nearly the same disruptions as the October 2013 shutdown of the federal government, which resulted in national parks closing, furloughs of hundreds of thousands of federal workers and a general sense of disgust with Washington dysfunction. If no deal is reached, the Department of Homeland Security will deem many workers essential – particularly those overseeing border security, airline safety, disaster responses and domestic terror assessments.

Many Republicans fear the public reaction would mirror October 2013, when Republicans tried to force Obama to accept a funding plan that would have gutted his landmark health-care law.

That shutdown cratered public support for Republicans, leaving them in a hole that took them almost a year to climb out of.