The Obama administration is "not bluffing" in its intent to take executive action on immigration policy if House Republicans don't act soon, top Democratic leaders warned Thursday.

President Obama has delayed any potential changes to his deportation policy to allow House GOP leaders time to bring legislation to the floor this summer. But if the Republicans don't act in July, the Democrats say, unilateral changes by Obama are inevitable.

"We're at the end of the line," Sen. Robert Menendez Robert (Bob) MenendezKasie Hunt to host lead-in show for MSNBC's 'Morning Joe' Senators ask for removal of tariffs on EU food, wine, spirits: report VOA visa decision could hobble Venezuela coverage MORE (D-N.J.) said Thursday during a press briefing in the Capitol. "We're not bluffing by setting a legislative deadline for them to act.

"Their first job is to govern," Menendez added, "and in the absence of governing, then you see executive actions."

Sen. Dick Durbin Richard (Dick) Joseph DurbinMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled Senate Republicans signal openness to working with Biden Top GOP senator calls for Biden to release list of possible Supreme Court picks MORE (D-Ill.) piled on. Noting that a year has passed since the Senate passed a sweeping immigration reform bill with broad bipartisan support, he urged House Speaker John Boehner (R-Ohio) to bring a similar bill to the floor.

"I don't know how much more time he thinks he needs, but I hope that Speaker Boehner will speak up today," Durbin said. "And if he does not, the president will borrow the power that is needed to solve the problems of immigration."

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The remarks come a day after Boehner announced his intent to push legislation allowing the House to sue Obama for what the Republicans say is a habitual inclination to overstep his constitutional authority.

"When there is a failure on the part of the president to faithfully execute the law, the House has the authority to challenge this failure," Boehner wrote Wednesday in a memo to House lawmakers.

Boehner did not name specific examples of alleged overreach, but Republicans have long been up in arms over Obama's 2012 program allowing some high-achieving illegal immigrants brought to the United States as kids to stay in the country and work without fear of deportation.

Sen. Charles Schumer (N.Y.), the third-ranking Democrat in the upper chamber, said Boehner and other Republican critics of Obama's executive actions have "a very good antidote" for their fears: "Put a bill on the floor."

"He's, like, shooting his parents and then throwing himself on the mercy of the court as an orphan," Schumer said. "Pass a bill, and that won't happen.

"If they don't bring any bill to the floor, the president has no choice — on a humanitarian basis and on a policy basis — to act where he can on his own," Schumer added.

Boehner on Tuesday said the current influx of immigrant children across the southern border will only make it tougher to pass legislation this year. The Speaker blamed Obama for the crisis.

"The president's making this harder and harder every day for us to try to deal with this in a responsible way," Boehner told reporters in the Capitol. "We've got a humanitarian disaster on the border. Most of it, at the president's own making, in my opinion, and so it makes our jobs much more difficult because of the actions he's taken or not taken with regard to the border."

Some immigration reformers have been hopeful that the recent shake-up in Republican leadership, which will have Rep. Kevin McCarthy (R-Calif.) soon replacing Rep. Eric Cantor (R-Va.) in the majority leader spot, could lead to action on immigration reform this year.

But McCarthy on Sunday seemed to throw cold water on that notion, telling Fox News that he plans to do "nothing about immigration until we secure the borders" — a sharp change from January, when he promoted "legal status" for illegal immigrants "that will allow you to work and pay taxes" without fear of deportation.

House Minority Whip Steny Hoyer Steny Hamilton HoyerHouse Democrats postpone vote on marijuana decriminalization bill Democrats scramble on COVID-19 relief amid division, Trump surprise The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (D-Md.) said Thursday that he spoke with McCarthy on Wednesday, urging the incoming majority leader to bring an immigration bill to the floor.

Hoyer did not reveal McCarthy's response.