WASHINGTON — The possible shutdown of the Department of Homeland Security threatens the Obama administration’s efforts to counter the extremist appeal of the Islamic State group within the U.S. – and to respond with emergency aid to communities struggling with winter snowstorms, Homeland Security Secretary Jeh Johnson warned Sunday.

In a round of appearances on network news programs, Johnson said that if Congress fails to agree on a new budget for his department by Friday’s end, lawmakers’ inaction would lead to staff furloughs that could hamstring U.S. responses to terrorist threats and warnings, such as the one late Saturday that names the Mall of America.

Johnson said that up to 30,000 DHS workers would have to be furloughed, including up to 80 percent of Federal Emergency Management Agency workers even as that agency contends with two months of devastating snowfall and cold from New England to the Mountain States.

“It’s absurd that we’re even having this conversation about Congress’ inability to fund Homeland Security in these challenging times,” he said.

After a week’s break, Congress returns to work Monday, just days before funding for DHS’ $40 billion budget ends. Lawmakers have until the end of the week to approve the budget and avoid shutting down the department, but no clear solution is in sight.

“The House has acted to fund the Homeland Security Department,” Kevin Smith, a spokesman for House Speaker John Boehner, said in an email Sunday. “Now it’s time for Senate Democrats to stop blocking legislation that would do the same.”

A House-passed bill would cover the department through Sept. 30 and overturn President Obama’s executive action to limit deportations for millions of immigrants in the United States illegally. But Senate Democrats are preventing a vote on a similar, Senate measure.

The issue was further clouded last week when a federal district court judge in Texas temporarily blocked the administration’s plans to protect immigrant parents of U.S. citizens or legal permanent residents from deportation. The decision came as part of a lawsuit filed by 26 states claiming Obama had overstepping his authority in taking the executive action. Johnson said the administration will appeal the ruling.

“We should have debate about immigration reform but you should not tie that to funding of the department,” Johnson said.

Two prominent Republican senators agreed. South Carolina’s Lindsey Graham and Arizona’s John McCain said Sunday they would oppose such a linkage. Graham said he was “willing and ready to pass a DHS funding bill and let this play out in court.”

Indeed, of Homeland Security’s 230,000 employees, some 200,000 would keep working even if Congress fails to fund their agency. They would receive no pay, however, until Congress authorizes funding. It’s a reality that was on display during the 16-day governmentwide shutdown in the fall of 2013, when national parks and monuments closed but essential government functions kept running, albeit sometimes on reduced staff.