Sen. Ted CruzRafael (Ted) Edward CruzWarren goes local in race to build 2020 movement Trump holds chummy meeting with Turkey's Erdoğan Overnight Defense: Trump hosts Erdoğan at White House | Says Turkish leader has 'great relationship with the Kurds' | Highlights from first public impeachment hearing MORE (R-Texas) pointed the finger at the Republican leadership for a delay in dealing with Homeland Security funding until the end of February and Senate Democrats for blocking a deal that would fund the agency while also defunding the president's executive actions on immigration.

"It's now up to leadership to lay out their strategy, I told them this was not a winning strategy and they went down this road," he said on CNN's "State of the Union," adding that he fought "tooth and nail" against the strategy.  

"What we saw last week was stunning irresponsibility from the Senate Democrats, the Senate Democrats three times filibustered funding."

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At the end of last year, Congress passed a budget omnibus for the entire government, but only authorized Homeland Security funding until the end of February. Republican leadership hoped that a new majority in Congress would have better leverage after lawmakers took office to pass a measure that would halt President Obama's move to provide work permits and delay deportations for millions of undocumented immigrants.

Cruz wanted to address the issue back in December and pass one bill that dealt with both government funding and what he sees as an overreach by Obama on immigration. 

But with just a month to go before the agency's funding runs out, Homeland Security Secretary Jeh Johnson warned against tying up the partisan immigration debate into budget politics at a time where the country faces a number of threats from terrorism, border security and more. 

“If people in Congress want to have the debate about immigration reform, let's have that debate. But don’t tie that to funding public safety and Homeland Security for the American people," he said just before Cruz on CNN. 

“This is not a situation to make light of. In these challenging times, we need a fully-funded Department of Homeland Security.”