(Bloomberg) — The U.S. Senate Republican leader changed strategy in the party’s attempt to block President Barack Obama’s immigration orders and avoid a partial shutdown of the Department of Homeland Security.

Majority Leader Mitch McConnell proposed legislation that separates the immigration issue from funding for the agency after the Senate failed Monday for a fourth time to advance a House-passed bill that linked the two matters. Funding for the department is set to expire Friday.

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McConnell of Kentucky said he was offering the bill as “a way to get the Senate unstuck.”

Republicans have insisted on using a $39.7 billion Homeland Security funding bill to reverse Obama’s decision in November to ease deportation for about 5 million undocumented immigrants in the U.S.

McConnell didn’t outline a strategy for funding the agency, though the immigration vote would clear the way for a separate funding bill sought by Democrats. McConnell has said repeatedly that he wouldn’t let the agency’s funding expire.

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The move distinguishes McConnell’s leadership style from that of House Speaker John Boehner, who has allowed the demands of Tea Party-aligned lawmakers to bring the government to the brink of a shutdown before reaching a compromise. A 16-day partial shutdown in October 2013 was triggered by a dispute over funding Obamacare.

Strategy Tug-of-War

McConnell and Boehner of Ohio have been in a tug-of-war over strategy. Two weeks ago, McConnell declared the Homeland Security bill “clearly stuck in the Senate” and said the next step was up to the House. Boehner, though, insisted “the House did its job” and the Senate must make the next move.

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Boehner’s spokesman Michael Steel said Monday that a separate vote on the November immigration orders “will highlight the irresponsible hypocrisy of any Senate Democrat who claims to oppose President Obama’s executive overreach on immigration, but refuses to vote to stop it.”

The new legislation will put pressure on Senate Democrats including Joe Manchin of West Virginia and Claire McCaskill of Missouri who have been critical of Obama’s immigration orders.

Democrats have been demanding a Homeland Security funding measure that doesn’t address the immigration orders.

“Time is running out, and the money is running out,” Maryland Senator Barbara Mikulski, the top Democrat on the Appropriations Committee, said Monday. “We can’t run out on homeland security. We’ve got to do our job and help them keep us safe and protect our country.”

Homeland Funding

Senator Charles Schumer, a New York Democrat, said McConnell’s proposal “doesn’t bring us any closer to actually funding DHS, and Republicans still have no real plan to achieve that goal.”

Obama told the nation’s governors that a shutdown of the agency will affect the economy and the nation’s security.

“These are folks who, if they don’t have a paycheck, are not going to be able to spend that money in your states,” Obama told members of the National Governors Association at the White House Monday. “It will have a direct impact on your economy, and it will have a direct impact on America’s national security, because their hard work helps to keep us safe.”

Homeland Security Secretary Jeh Johnson said a shutdown would require 75 percent to 80 percent of his employees, including border patrol agents and members of the Coast Guard, to work without pay. The department would have to furlough 30,000 employees, including much of the headquarters staff.

‘One Step’

“Every day I press the staff at my headquarters to stay one step ahead of groups like ISIL and threats to our aviation security,” Johnson said in a news conference Monday, referring to the terror group Islamic State. “If we shut down, that staff is cut back to a skeleton.”

While Republican leaders were trying to pin the blame on Democrats, some Republicans warned that their party would shoulder the responsibility for any disruptions.

“For God’s sakes, don’t shut down the premier homeland security defense line called the Department of Homeland Security,” Senator Lindsey Graham of South Carolina said Monday on the “Fox & Friends” program. “If we do, as Republicans, we’ll get blamed.”

A new CNN/ORC poll showed that 53 percent of Americans would blame Republicans in Congress for a shutdown, while 30 percent would blame Obama. A majority said a shutdown, even for only a few days, would be a crisis or a major problem.

Boehner, asked in a “Fox News Sunday” interview aired Feb. 15 whether he was prepared to let the department’s funding lapse, said, “Certainly. The House has acted.”

The Senate vote Monday that failed to advance the House bill was 47-46 with 60 required.

Fiscal Year

Congress has funded the rest of the federal government through the end of the fiscal year Sept. 30. The House bill, H.R. 240, would fund the Homeland Security agency through the same period.

During the 16-day partial government shutdown in October 2013, many Homeland Security employees remained on the job because they were considered essential. That includes active Coast Guard members, customs officers, immigration law enforcement officers and airport-screening officials.

Other employees were placed on furlough. The department has estimated that a partial shutdown would affect about 5,500, or 10 percent, of workers in the Transportation Security Administration, mainly in management and administrative jobs.

Delayed Pay

In 2013, about one-third of the government’s 3 million workers who reported for duty weren’t paid until after the shutdown ended.

Separately, the Obama administration Monday asked a Texas judge to suspend an order that forced the White House to delay carrying out its immigration plans during a court challenge by Texas and 25 other states.

The administration gave U.S. District Judge Andrew Hanen in Brownsville, Texas, until the close of business Wednesday to act on his own before it goes directly to an appeals court in a bid to temporarily set aside his order.

To contact the reporter on this story: Heidi Przybyla in Washington at hprzybyla@bloomberg.net

To contact the editors responsible for this story: Jodi Schneider at jschneider50@bloomberg.net Laurie Asseo

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• President Barack Obama
• Mitch McConnell