Washington (CNN) Senate Majority Leader Mitch McConnell announced he is changing tactics in an attempt to break a stalemate with Democrats ahead of Friday's deadline when the Department of Homeland Security will run out of money, after taking his fourth failed vote on a House-approved measure.

On a measure that needed 60 votes to succeed, it failed with 47 voting in support to 46 against.

McConnell said he would bring a separate bill to the floor this week that would block funding for the implementation of President Barack Obama's immigration executive orders -- provisions in the current DHS bill that Democrats object to.

By separating the immigration matter from the DHS funding bill, McConnell hopes to satisfy conservatives by allowing them to vote against the immigration orders while allowing a so-called "clean" DHS bill possibly to move on a separate track.

While it's too early to know if the new plan will work -- and there are many procedural hurdles that could doom it -- it's the first new idea in weeks to break the congressional logjam over DHS.

Republicans also believe it will put on the spot a handful of centrist Democrats who raised concerns with the immigration orders but have so-far refused to vote against them as long as they were attached to the DHS bill.

"Some Democrats give the impression they want Congress to address the overreach," McConnell said. "But when they vote, they always seem to have an excuse for supporting actions they once criticized. So I'm going to begin proceedings on targeted legislation that would only address the most recent overreach from November. It isn't tied to DHS' funding. It removes their excuse."

Sen. Chuck Schumer of New York, used the failed vote as an opportunity to blame Republicans for failing to fund the agency.

"It's becoming clear Sen. McConnell realizes he must separate himself from the far right, but the bottom line is this proposal doesn't bring us any closer to actually funding DHS, and Republicans still have no real plan to achieve that goal," he said.

It's not apparent how many Democrats might be persuaded to vote against the immigration orders in a standalone bill and whether it would be enough to give Republicans the 60 votes they need to get over procedural hurdles. It is unlikely supporters could get the 67 votes needed to overcome a veto, which surely would come from the President should the legislation clear Congress.

Before Monday's vote, Senate Democrats squabbled with House Republicans about who exactly was to blame for the ongoing standoff.

There are only four days before DHS funding ends, which will leave large parts of the agency shuttered or employees will be forced to work without pay.

"We passed a bill that fully funds the department," House Homeland Security Committee Chairman Michael McCaul, R-Texas, said in an interview on CNN. "We'll probably see something come from the Senate this week and we'll have to make some tough choices. It would be irresponsible for lawmakers and policy-makers to shut down his national security agency at this grave time."

Sen. Claire McCaskill of Missouri urged her colleagues, via Twitter, to pass a funding measure to "show unity against terrorists."

"Let's pass funding for Homeland Security today to show unity against terrorists," McCaskill tweeted. "Then R's can bring up immigration for vote immediately after."

Let's pass funding for Homeland Security today to show unity against terrorists.Then Rs can bring up immigration for vote immediately after. — Claire McCaskill (@clairecmc) February 23, 2015

But DHS is still prepping for the worst case scenario. In a letter to employees, Homeland Security Secretary Jeh Johnson said the department was making preparations "in the unlikely and unfortunate event that Congress does not fund DHS before Friday night a shutdown of this department occurs."

"Have faith that his difficult and unnecessary situation will be resolved," Johnson said.