After conservatives on Thursday brought down House Speaker John Boehner’s bill to address the border crisis, the new House Republican leadership team issued a joint statement declaring that President Obama should fix the problem himself.

“There are numerous steps the president can and should be taking right now, without the need for congressional action,” the leadership quartet proclaimed, “to secure our borders and ensure these children are returned swiftly and safely to their countries.”

Who’s in the what now?

Just the day before, House Republicans had voted to sue Obama for using his executive authority. They called him lawless, a usurper, a monarch, a tyrant — all for postponing deadlines in the implementation of Obamacare. Now they were begging him to take executive action to compensate for their own inability to act — even though, in this case, accelerating the deportation of thousands of unaccompanied children coming from Central America would likely require Obama to ignore a 2008 law.

This was not a momentary lapse but a wholesale upending of reason.

Rep. Hal Rogers (R-Ky.), the Appropriations Committee chairman who had been leading the GOP side in the border legislation debate, told reporters much the same thing after the legislation was pulled from the floor. “I think this will put a lot more pressure on the president to act,” he told The Post’s Ed O’Keefe and other reporters. “He has the authority and power to solve the problem forthwith.”

Apparently, if Obama is using his executive authority to advance a policy House Republicans support, it’s a meritorious exercise of presidential authority; if he uses that same authority to aid a policy they oppose, it’s time to write up articles of impeachment.

In another action this week, Republicans acknowledged, at least tacitly, that Obama has the executive authority to postpone deportations. The House majority drafted legislation that would forbid the executive branch from anything that would “expand the number of aliens eligible for deferred action.”

But in proposing such legislation (which was pulled from the floor Thursday but then approved Friday night) Republicans implicitly acknowledged that Obama has such power now. Therefore, until both chambers of Congress can pass such a law by veto-proof margins, Obama retains the power. This is probably why House Republicans, just two weeks earlier, scoffed at the suggestion that they pass this sort of legislation when the idea came up before the Rules Committee.

If the GOP position sounds contradictory, that’s because it’s less about the Constitution than cleavages within the party. There are real questions about Obama’s abuses of power — say, the spying on Americans by the National Security Agency or the use of drones to kill U.S. citizens overseas — but the opposition party has left those largely untouched. The planned lawsuit was a bone thrown to conservatives to quiet their impeachment talk. The legislation restricting Obama’s executive authority on immigration was a similar effort to buy off conservatives who had been encouraged to rebel by Sen. Ted Cruz (R-Tex.).

But the efforts to placate conservatives aren’t working. The new House GOP leadership team took over Thursday, but a mere two hours after Rep. Eric Cantor gave his valedictory as majority leader on the House floor, his successor did a face-plant.

All morning, GOP leaders had been predicting that they had sufficient Republican votes to pass Boehner’s border bill. But then conservatives, under pressure from Cruz and far-right interest groups, began to go squishy, and the new leader, Kevin McCarthy, announced that he was pulling the border bill from the floor and that members could depart early for their five-week summer break.

What followed was as close as Congress gets to one of those fistfights in the Taiwanese parliament. Mainstream Republicans besieged Boehner and McCarthy on the House floor, noisily demanding that they do something about the border crisis before going on holiday. Half an hour later, McCarthy announced that “additional votes are possible today.”

Boos and jeers rained down on the new leader. The speaker pro tempore, Virginia Foxx (R-N.C.), banged the gavel violently for order. Some lawmakers had to be called back from National Airport.

The hapless new majority leader, and his equally hapless new majority whip, Steve Scalise, called Republicans to an emergency meeting, where after fierce argument it was decided . . . that they would meet again on Friday.

Boehner, earlier in the day, tried to be philosophical. “I take my job one day at a time,” he said.

The problem with day-by-day leadership, though, is inconsistency: What you do on Thursday has a way of contradicting what you said on Wednesday.

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