Washington (CNN) House and Senate Republicans aren't getting any closer to bridging their differences over funding for the Department of Homeland Security. 
 
 House Speaker John Boehner again insisted on Sunday that the "House has done its job" and the cards are in the Senate's hands, Sens. John McCain and Bob Corker urged their fellow Republicans pass a bill without letting the agency's funding lapse. McCain pressed for a measure that will fund the homeland security agency without wading into the choppy political waters of immigration. 
 
 READ: Republicans struggle to avoid Homeland Security shutdown 
 
 House Republicans have already passed a bill to fund the Department of Homeland Security, but that bill is dead on arrival in both the Senate and on President Barack Obama's desk because it would also reverse his executive actions on immigration aimed at shielding millions of undocumented immigrants from deportation. 
 
 McCain, the chairman of the Senate Armed Services Committee, said "it would be terrible" for funding for the agency to wither because of a political fight over Obama's executive action. 
 
 "There are ways we can address what the President, did [which] was unconstitutional, but it's not through shutting down the Department of Homeland Security," McCain said Sunday on NBC's "Meet the Press." "It's too serious." 
 
 The fight over funding the agency comes at a time of heightened concerns over terror threats in the wake of terrorist attacks in Western cities and a foiled terror plot in Canada this week. And on Saturday, a shooting in Copenhagen, Denmark, also appeared to have been a terrorist act. 
 
 "The American people didn't give us the majority to have a fight between House and Senate Republicans," McCain said. 
 
 But Boehner, under pressure from a coalition of ardent conservatives in the House, was steadfast in an interview Sunday on Fox News Sunday. 
 
 "The Constitution makes it pretty clear that the House has to do its work and the Senate has to do theirs. The House has acted to fund the department and to stop the President's overreach when it comes to immigration and his executive orders," Boehner said. "It's their turn." 
 
 That's a stark contrast from what Senate Majority Leader Mitch McConnell said earlier this week. 
 
 "It's clear we can't go forward in the Senate" on a bill that would reverse Obama's immigration actions, he said. 
 
 Boehner, however, said he is prepared to allow funding for the Department of Homeland Security to run out, and said Senate Democrats should be blamed if that happens. 
 
 "Senate Democrats are the ones standing in the way, they're the ones jeopardizing funding, why don't they get on the bill or offer an amendment, offer their ideas," Boehner said. 
 
 In a statement Sunday reacting to Boehner, Sen. Chuck Schumer said Boehner was misreading the political optics of his maneuvering. 
 
 "When Speaker Boehner tied immigration to DHS funding he knew exactly what he was doing, saying, 'Unless I get my way, I'm going to shut down a large part of the government,'" said Schumer, a Democratic messaging leader. "To now blame Democrats when members of his own party, conservative leaders and others, have all asked him to back off this game of chicken is disingenuous at best." 
 
 Indeed, even fellow Republican, Senate Foreign Relations Committee Chairman Bob Corker, said on CBS's "Face the Nation" that allowing the agency shut down was not an option. 
 
 "I'll be the first to say when we have a department whose mission is to protect the homeland especially in these times, we need to fund it," Corker said. "It needs to be funded, we do not need to leave our nation in a situation with the type of threats that we have with an agency that's not working at full steam. It needs to be resolved and I think it will be." ||||| Pressed on whether he would, in effect, allow the department to shut down if the Senate does not come up with a funding bill of its own, the speaker said: “Certainly. The House has acted.” 
 
 Advertisement Continue reading the main story 
 
 In dispute is how to handle the issue of immigration. Last month, House Republicans passed a spending plan for the 240,000-employee department that included provisions to gut President Obama’s immigration policy. The bill would revoke legal protections for millions of unauthorized immigrants, including children, and put them at risk of deportation. 
 
 The House measure stands no chance of becoming law. Senate Democrats have filibustered it; Mr. Obama has said he would veto it; and even some Senate Republicans, including John McCain of Arizona, have questioned the wisdom of the House’s unyielding position, raising doubts that the bill would get even 51 Republican votes in the Senate. 
 
 A statement issued by a spokesman for Representative Nancy Pelosi, the House Democratic leader, said on Sunday that all of her caucus would vote for a “clean” Homeland Security bill — one that contained no immigration-related amendments — and urged the speaker to bring such a measure to a vote. 
 
 Newsletter Sign Up Continue reading the main story Please verify you're not a robot by clicking the box. Invalid email address. Please re-enter. You must select a newsletter to subscribe to. Sign Up You agree to receive occasional updates and special offers for The New York Times's products and services. Thank you for subscribing. An error has occurred. Please try again later. View all New York Times newsletters. 
 
 “Speaker Boehner made it clear that he has no plan to avoid a government shutdown that would threaten the safety of the American people,” the statement released by the spokesman, Drew Hammill, said. It called Mr. Boehner’s remarks “a sad reflection of the fact that the Tea Party continues to hold the gavel as they insist on their futile anti-immigrant grandstanding.” 
 
 Lawmakers are gone from Washington until next week, meaning that they have just four days in the Capitol in which to reach a deal before the department’s funding runs out on Feb. 27. 
 
 Mr. Boehner also spoke Sunday about another issue that has become a distraction: his invitation to Prime Minister Benjamin Netanyahu of Israel to speak before a joint meeting of Congress. The offer has prompted outrage in Israel and the United States from critics who say both leaders are using the speech for political gain. 
 
 Mr. Boehner said he had not consulted with the White House because he had wanted to make sure it did not interfere. 
 
 “There’s no secret here in Washington about the animosity that this White House has for Prime Minister Netanyahu,” he said. “And I frankly didn’t want them getting in the way and quashing what I thought was a real opportunity.” 
 
 Though Mr. Netanyahu has faced complaints at home as he campaigns for another term, he has declined to cancel the speech, which is set for March 3.
– If the Department of Homeland Security is forced to shut down at the end of this month because of a lack of funding, John Boehner says he's ready to let that happen and it won't be his fault. In an interview with Fox News Sunday, the House speaker said the House has already done its job, and he is "certainly" prepared to let Homeland Security funding lapse if Senate Democrats refuse to pass a bill that funds the department but also reverses President Obama's actions on immigration, reports the New York Times, which notes that lawmakers have just four working days left this month to reach a deal before funding runs out. Senate Democrats, who have filibustered the spending bill, "are the ones jeopardizing funding," Boehner said. "Why don't they get on the bill and offer an amendment, offer their ideas." But fellow Republicans including Sen. John McCain say allowing a Homeland Security shutdown is not an option, and Democrat Chuck Schumer issued a statement yesterday saying it was "disingenuous" for Boehner to "blame Democrats when members of his own party, conservative leaders and others, have all asked him to back off this game of chicken," CNN reports. If funding does run out, around 200,000 of Homeland Security's 230,000 employees are considered vital workers who will have to stay on the job even if Congress can't agree on a way to pay them, the AP reports.