But when Democrats heard the news, they were not impressed. Senate Minority Leader Harry Reid said that he had a positive meeting with McConnell on Tuesday, but then asked for more: House Speaker John Boehner's guarantee that the clean DHS funding bill could pass the House.
That's a tall order for Boehner, who will meet with his conference to discuss their options on Wednesday. It's likely that a clean DHS funding bill will earn the vast majority of Democratic votes in the House, but with conservatives riled up about the immigration measure, it will be a much harder sell in Boehner's own conference.
McConnell told reporters Tuesday, "I do not know what the House will do."
McConnell spokesman Don Stewart would not say whether McConnell had told Boehner about his new strategy before making the announcement Monday night, although he acknowledged that the two leaders speak often.
Sen. Jeff Flake, R-Ariz., said McConnell announced the decision at a conference luncheon Tuesday, but that the announcement had drawn ire from more-conservative members who believe McConnell was giving in to Democratic demands without holding the president accountable. Multiple Republicans in the meeting said there was still broad disagreement as to whether a caving to Democrats demands for a clean funding bill was the best course forward.
"Most of us feel like the courts gave us a major victory," Sen. Bob Corker, R-Tenn., said outlining the rationale for McConnell to offer a clean DHS bill now after weeks of not backing down. "Sometimes it makes a lot of sense to bank victories and move ahead."
Sen. Jeff Sessions, R-Ala., who has been a major advocate of tying DHS funding to blocking Obama's actions, says he thinks leadership should stick with the original plan.
"I think it is a big deal of huge, historic importance," Sessions says." I will be glad to consider what our leaders have talked about, but I remain firmly convinced that at this point Congress should put the heat where it belongs, and that is on the president."
Outside conservatives, who have been known to influence Boehner's ability to get his conference to "yes" have already said they are opposed to stand alone DHS funding bill. Senate Conservatives Fund tweeted Tuesday, "Senate GOP leaders surrender again "¦ plan to fund Obama's amnesty for the rest of the fiscal year."
The influence, especially of a group such as Heritage Action for America, which announced it will key vote a "no" on a clean DHS funding vote, could still derail any DHS deal. "As the majority leader said last year, the power of the purse is the 'only tool' Congress has to rein in executive overreach," Heritage Action CEO Michael Needham said in a statement.
"I think it is clear that the House has not agreed on a strategy yet," Flake told reporters.
For Democrats, the only way to pass a DHS bill is without amendments defunding Obama's unilateral actions. "Separation's important," Senate Minority Whip Dick Durbin said after the press conference, "and the order if it's going to be accomplished before the deadline really requires us to move to the funding bill first."