WASHINGTON — Majority Leader Mitch McConnell declared a Senate stalemate Tuesday over immigration provisions attached to a Homeland Security spending bill, and called on the House to make the next move to avoid an agency shutdown.

House Republicans said they had no intention of doing so, leaving Congress at an impasse with no clear way forward barely two weeks before the agency’s $40 billion budget shuts off.

“I can tell you I think it’s clearly stuck in the Senate,” McConnell, R-Ky., told reporters after a closed-door lunch of Senate Republicans. “And the next step is obviously up to the House.”

Michael Steel, spokesman for House Speaker John Boehner, responded with a statement seeking to put the focus on Senate Democrats. Democrats voted three times last week to block a House-passed bill that funds the department for the remainder of the budget year while also overturning President Barack Obama’s executive actions limiting deportations for millions here illegally.

“Until there is some signal from those Senate Democrats what would break their filibuster, there’s little point in additional House action,” Steel said. Democrats say they can’t accept the bill unless the contested language on immigration is removed.

The impasse comes with Homeland Security funding set to expire Feb. 27 without action by Congress. The most likely outcome may be a short-term extension of current funding levels, something Homeland Security Secretary Jeh Johnson is urging Congress to avoid because it would prevent the agency from going forward with a host of planned initiatives, from improvements at the Secret Service to new security technology on the U.S.-Mexico border.

“I’m urging every member of Congress that I can meet, Democrat and Republican, to figure out a way to break this impasse so I can get a fully funded bill by Feb. 27,” Johnson told reporters Tuesday on the way out of a meeting with senators.

The fight over immigration and the Homeland Security spending bill is a major early test for Republicans who took full control of Congress in January for the first time in eight years. Democrats are already gleefully declaring that the GOP is failing the test, but with Republicans six votes shy of the 60 needed to advance most legislation in the Senate, they say there’s little they can do if Democrats won’t budge.

“The Democrats are filibustering it. I don’t know how we get blamed for that this time,” said Sen. Orrin Hatch, R-Utah. “Everybody knows it takes 60 votes to do anything.”

House Republicans, for their part, are frustrated that even now that the Senate is in GOP hands, they are still being asked to fold to Democratic demands.

“A hundred senators got elected to say they wanted to solve problems,” House Majority Leader Kevin McCarthy told reporters ahead of McConnell’s comments Tuesday. “They didn’t get elected to say, ‘We’ll wait and see what the House does.’ They should show us where they stand.”