House Republicans disagree. Speaker John Boehner has said repeatedly that the House has already acted to fund the Homeland Security Department and that the ball is now in McConnell's court.
That message did not change from last week. House Majority Leader Kevin McCarthy hosted all committee chairmen in his office Tuesday afternoon, during which the topic was discussed. But exiting the meeting, relevant chairmen stood firm, saying, with annoyance, that the onus to act is still on the Senate.
"You can do anything you want to up there. They are the Senate, they are all-powerful. They are all-knowing," said Rep. Rob Bishop, R-Utah.
House Appropriations Committee Chairman Harold Rogers said that House has acted and the Senate should send a bill back to his chamber. Similarly, House Homeland Security Committee Chairman Michael McCaul said the Senate still has legislative options, including a compromise proposal by GOP Sen. Susan Collins of Maine.
"We don't think the Senate's done with their job quite yet," McCaul said. "The Senate has failed in their responsibilities, and that's unfortunate. We're still going to continue to push them. We think they have a few additional measures they're looking at to try to move the ball forward."
Others in the House, however, are ready to move on. Rep. Charlie Dent, R- Pa., emphasized that with time running out there are really only two options left that could get the votes to pass Congress. If the Senate cannot reach an agreement, the House would be forced to send over either a continuing resolution to keep the department from shutting down or a clean DHS funding bill.
With House and Senate Republicans caught in that game of hot potato, and Senate Democrats refusing to move forward on anything but a clean bill, the word "shutdown" has begun to grace some lips in the Senate Republican Conference.
Members insist that, should they miss the funding deadline, Democrats will earn the blame. "I don't know how we get blamed for that this time. "¦ Who else could get blamed? We're not the ones filibustering," GOP Sen. Orrin Hatch of Utah said Tuesday.
Republican Sen. Mark Kirk, who is up for reelection in blue Illinois in 2016, was more direct. "If they're cynically trying to restart the government-shutdown battle, they should be blamed directly. "¦ It's a very dangerous game. If we have a successful terrorist attack—all the dead Americans from that should be laid at the feet of the Democratic caucus," Kirk said.
To avoid a shutdown, members could pass a short-term continuing resolution to keep the department funded at its current levels while Republicans consider their options on immigration. Democratic leaders called that a "bad" strategy in a press conference Tuesday, but did not rule out supporting a clean, short-term bill. "We much prefer to do full funding," Sen. Chuck Schumer said.