As the Congress begins a new work week, there are no signs that lawmakers are anywhere near a final resolution on how to handle the budget for the Department of Homeland Security, as Republicans continue to push a funding measure that also blocks recent executive actions on immigration by President Obama.

Three days in a row last week, Democrats sustained a filibuster in the Senate against that DHS spending bill, refusing to allow the House-passed GOP plan to even be brought up on the floor for debate and amendments, hotly opposed to the Republican effort on immigration.

"It really doesn't make sense," said Senate Majority Leader Mitch McConnell (R-KY), who found himself on the opposite end of a filibuster after slowing Democrats with such parliamentary maneuvers over the past eight years.

"I don't understand why they would block the Senate from even debating," McConnell said last week.

As for Democrats and their new love for the filibuster, they repeatedly made clear they won't back down, arguing the immigration restrictions should be addressed separately, and not put the Homeland Security Department on the edge of a possible shutdown.

"Pass a clean homeland security bill," said Sen. Charles Schumer (D-NY), who also declared, "we will not be held hostage," as Democrats tried to argue that Republicans would be the ones responsible for any shutdown, an argument that GOP Senators firmly rejected.

It was unclear whether there would be more procedural votes in the Senate this week related to the immigration dispute; the deadline for action is February 27, but with the Congress scheduled for a break next week, there really aren't that many days to reach a deal.

"I'm sure we'll resolve this sometime in the next few weeks," McConnell said.

What if DHS shuts down?

While Democrats and the White House have been warning against a failure to extend the budget of the Department of Homeland Security, much of that sprawling federal agency would actually continue to operate if there is a shutdown - except most of the employees wouldn't get paid.

That's what happened in the shutdown of October 2013, when over 85% of DHS employees kept going to work - DHS has about 230,000 workers; about 200,000 of them still had to get to their jobs during that period without an operating budget.

This from the Associated Press on why a shutdown would not have a giant impact on DHS:

That's because most department employees fall into exempted categories of workers who stay on the job in a shutdown because they perform work considered necessary to protect human life and property. Even in a shutdown, most workers across agencies, including the Secret Service, Transportation Security Administration, Federal Emergency Management Agency and Customs and Border Protection, would continue to report to work.

Airport security checkpoints would remain staffed, the Secret Service would continue to protect the president and other dignitaries, the Coast Guard would stay on patrol, immigration agents would still be on the job.

While some workers might have to go without paychecks, there are some entities within DHS where operations are funded mainly by fees - so they would continue to be paid.

What is one of the organizations within DHS that is mainly funded by fees? The folks doing work at the U.S. Citizenship and Immigration Services - those responsible for implementing the President's executive actions on immigration, which would lift the threat of being deported for about 4-5 million people who are in the U.S. illegally.

So, the irony of this fight is this - if the Homeland Security Department shuts down on February 27, the work goes on at the one office where Republicans really want it to stop - on immigration.