Rep. Ruben Gallego, an Arizona Democrat who is co-sponsor of a Homeland Security bill that explicitly omits amendments on immigration, on Thursday described his measure as one that centers on keeping families together.

“The Democratic party is keeping families together, and win or lose politically, we know we’re doing the right thing,” Gallego told Fox News Latino.

Gallego joined as co-sponsor of what Democrats called a “clean DHS funding bill,” which was introduced this week by Reps. Lucille Roybal-Allard of California and Nita Lowey of New York.

Gallego and Robyal-Allard say that their measure, which House Republicans blocked a vote on, is free of the GOP “anti-immigrant poison pills.”

Meanwhile, Republicans say Senate Democrats are being petty by blocking a debate on a GOP-led DHS funding bill that passed in the House.

On Thursday, Sen. Ted Cruz, a Texas Republicans, said Democrats were being “reckless and irresponsible.”

Conservative Republicans are in a pitched battle with the Obama administration, and many Democrats, over amendments included in a Homeland Security spending bill that the House recently passed. Those amendments defund executive orders that the president established last year that would suspend deportation for potentially 5 million undocumented immigrants.

The executive orders expand the number of people who qualify for a 2012 initiative for relief from deportation by removing certain restrictions, such as age limits, and other things. President Barack Obama also extended deportation relief – for three years – to undocumented immigrants who have children who are U.S. citizens or legal permanent residents.

Republicans accuse Obama of overreach in his unilateral move to suspend deportations, and have threatened to sue him for actions that they say are unconstitutional.

The House DHS bill failed to gain traction in the Senate, however, after Democrats blocked a vote that would have paved the way for a debate on the measure and then a vote on it.

Each party is accusing the other of playing politics and putting the nation’s security at risk by holding up funding of DHS. A spending bill must pass by Feb. 27 to keep the agency fully functional.

“There are 17 days left until DHS runs out of funds putting our national security at risk,” Gallego said. “This is no time to play with our country’s safety, the American people elected us to work on their behalf and the safety of our country should not be a partisan or political issue.”

Gallego said that if Republicans object to Obama’s executive actions, there are ways to address them outside of the DHS spending bill.

“If they believe it’s unconstitutional, you let it work its way through the Supreme Court,” he said, “or pass a comprehensive immigration reform bill to give legal status instead to a lot of these families that have temporary status now.”

Gallego said Republicans cannot "hold Democrats hostage and separate families," in reference to families that have been separated through deportations.

On Thursday, Sen. Ted Cruz and Rep. Bill Flores, both Texas Republicans, blamed Democrats for playing political games and using DHS as a pawn, according to the Dallas Morning News.

Cruz rejected suggestions by some Republicans that the Senate change rules so that Democrats could not continue to block measures such as the DHS one from moving forward.

“The answer is not to change Senate rules,” Cruz said at a press conference held by House and Senate conservatives. “The answer is for Senate Democrat not to be obstructionists.”

“We are in a time of growing threats at home and abroad,” Cruz said. “And for Senate Democrats in a partisan vote to filibuster funding for the Department of Homeland Security is both reckless and irresponsible.”

Flores said that Senate Democrats should “do your job. Uphold the oath that you took to defend the Constitution.”

Gallego said that Republicans have only themselves to blame for the DHS funding logjam.

"At the end of the day, it's the GOP process that corrupted the bill to begin with," he said, "then they found themselves in a situation where they're looking at us to get them out of the problem that they caused."