"[McConnell] has moved this bill forward; he has stood firm that we should bring it to the floor, that we should pass it," said Sen. Jeff Sessions of Alabama, who has been known to rally conservatives in the House around immigration causes. "He's done the right thing."
Republicans lament that while Democrats want to whine about what is in the legislation, they are not willing to vote to move the bill forward where amendments would be possible.
"Is there anything wrong with just discussing it?" asked Sen. Chuck Grassley of Iowa. "I think that the public has to know that the Democrats don't want to discuss what the president did last November."
But patience among some of the more moderate members of the caucus, those who want to exhibit the party's propensity to govern, may be starting to wear thin.
"Is that the definition of insanity? Voting for the same bill over and over again?" Sen. John McCain asked.
Sen. Jeff Flake of Arizona, who worked on the bipartisan immigration bill that passed the last session of Congress, says it's up to McConnell, but he's not sure the DHS funding bill is the best time to have an immigration debate.
"My preference has always been to address Obama's action with legislation," Flake said. "I think we see the end of this movie."
Sen. James Inhofe of Oklahoma does not expect to find resolution with this tactic. At some point, he says, Republicans will have to find a new way forward.
"I think three is enough," Inhofe said. "There is going to be an effort to keep bringing it up and keep the issue alive, and as you know there is division within the conference on this."
In upcoming days, McConnell may find himself beginning to be boxed in as he has to continue to quell the conservatives without risking more defections from the moderates in his conference. Some say that the repeated votes may be nothing more than a way for McConnell—who has a reputation for making deals—to show his right flank that he's willing to go to the mat for legislation, but he may also end up making a point to some in his caucus that even with a new majority, the party cannot get exactly what it wants.
"We understand what the House did, but we hope they understand our constraints as well. But we cannot shut down the Department of Homeland Security, with the threats that we have from ISIS and overseas," McCain said.
As the deadline looms, Sen. Susan Collins of Maine was trying to find a way to break the Democratic filibuster. She offered an amendment Wednesday to strip the House bill of the contentious repeal of the president's 2012 executive action, hoping it might get some Senate Democrats to vote to move onto the bill. But Democratic moderates were not interested.
"DHS is something that should be a clean bill. I have always said that," said Sen. Joe Manchin, a Democrat from West Virginia who has been known to cross the aisle on key votes, when he was asked whether he would support moving forward with the DHS funding bill if the Collins amendment was promised. He said he'd take a look at it, but that he believed it needed to stand alone. "I am willing to debate immigration or anything else separate, but not under these circumstances."
But Rep. John Carter of Texas, chairman of the House Homeland Security Appropriations Subcommittee, said that he would be open to a DHS funding bill that targeted only the latest executive action.
"Politically, [McConnell] needs to make a lot of noise. Because the constituency is very upset about that November surprise," Carter said. "If we have to compromise, the fight is on November."