But like the three votes before it, Senate Democrats are expected to block taking up the bill that passed the GOP-controlled House because it contains what they consider poison pills -- provisions that would block President Barack Obama's executive orders on immigration.

Boehner tells the Senate to pass DHS funding 00:27

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READ: What happens if DHS shuts down?

With only four days before DHS funding ends -- when large parts of the agency will be shuttered or employees will be forced to work without pay -- the two sides are at a stalemate and there are no known serious negotiations involving congressional leaders or the White House to bridge differences.

"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."

While it wasn't clear what McCaul expects back from the Senate -- since the chamber can't even take up a bill right now -- the chairman warned that with the recent surge in deadly terrorist attacks abroad, "It would be irresponsible for lawmakers and policy-makers to shut down his national security agency at this grave time."

Democrats hoped a recent ruling from a federal judge in Texas blocking, at least temporarily, implementation of the President's most recent immigration orders, would give Republicans a reason to fund the department while the issue plays out in court. But there was little evidence GOP lawmakers would do so.

In fact, Republicans continued to try to pressure centrist Democrats, some who have not fully embraced the President's immigration orders, to change their minds and vote to block Obama from carrying them out.

House Republicans from Virginia wrote a letter to the state's two Democratic senators, Mark Warner and Tim Kaine, urging them to approve the House bill.

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"On behalf of the people of the Commonwealth of Virginia, we urge you to reconsider your votes to protect President Obama's unlawful executive action," the eight lawmakers wrote. "We regard the President's recent action as an affront on our power as legislators, and, by extension, the representation promised to our constituents by our founding fathers."

But there were no signs any of the Democrats were persuaded.

"Let's pass funding for Homeland Security today to show unity against terrorists," one of the targeted Democrats, Sen. Claire McCaskill of Missouri tweeted. "Then R's can bring up immigration for vote immediately after."

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.