Here’s a paradox worth pondering: Could President Obama’s executive action on immigration actually make it easier to enact comprehensive reform?

The invective pouring forth from Republicans last week would seem to suggest not: “deliberately sabotage any chance of enacting bipartisan reforms . . . trying to pick a bar fight . . . throwing this nation into a crisis . . . anarchy.” Mitt Romney, the failed 2012 Republican presidential nominee, told CBS’s Bob Schieffer that Obama was “poking an eye of the Republican leaders in Congress.”

The natural instinct is to poke back — an eye for an eye. But one Republican, at least, has a better idea. “Rather than poke him in the eye, I’d rather put legislation on his desk,” Sen. Jeff Flake (R-Ariz.) told me Thursday.

The idea of Congress legislating seems quaint these days, but Flake’s counterintuitive view is that Obama’s unilateral action will increase pressure on the president to accept conservative immigration bills and therefore will increase the odds that something resembling comprehensive immigration reform will be enacted. “I think it will be easier in a sense,” he said.

Flake is a conservative in good standing, and he opposes the executive action as much as the next Republican. Elected to the Senate in 2012 after a dozen years in the House, he has a 95 percent lifetime rating from the American Conservative Union. But he’s also a reasonable man; he was a member of the Gang of Eight that crafted the original Senate compromise on immigration. And this border-state legislator thinks it’s stupid to shut down the government in an effort to undo Obama’s immigration order. As for the lawsuits against Obama? “Background noise,” he said.

Instead, Flake proposes letting the action stand — and even offering to make it permanent — if Obama first makes the three concessions that Republicans have long sought on immigration. His hunch is that Obama, to quell the Republican rage on immigration and to make his executive action permanent, would ultimately take that deal.

First, Flake wants the House, followed by the Senate, to pass a border security bill with tougher standards than the Senate compromise, requiring a 90 percent apprehension rate at the border before any permanent legalization of undocumented immigrants. Obama, who has just stretched the limits of his constitutional authority to protect undocumented immigrants, “would be harder-pressed to veto a border security bill, a tough one, than he would have before,” Flake figures.

Next, the Republican Congress would send Obama a bill with tougher interior enforcement of immigration, including a mandatory “e-verify” program. Third, Congress would send Obama legislation covering visas for temporary and high-tech workers. Some Democrats would object to both, but Obama would find them “tougher for him to turn down now” after the furor stirred by his executive order.

Then, and only then, would Congress send Obama legislation giving his executive action the force of law and providing a path to citizenship for undocumented immigrants. Flake admits that will still be opposed by many Republicans as so-called amnesty. But he thinks he can win over enough of them after giving them the piecemeal approach to immigration reform they insisted on.

Obama and the Democrats may regard the first three bills as legislative eye pokes, but the president, who picked this latest fight with his executive action, has a powerful incentive to make concessions now: His action offers temporary protection from deportation to 3.7 million undocumented immigrants, but without congressional approval, it doesn’t put anybody on a path to citizenship, and it can be erased by a future president.

Is the Flake plan naive? Perhaps. Flake, telegenic and amiable, occasionally lives up to his name, most recently filming a reality survival show on a deserted island with Sen. Martin Heinrich (D-N.M.). When seeking out a quiet place for us to talk Thursday off the Senate floor, he wandered into a room where the Senate Democratic caucus was meeting with White House chief of staff Denis McDonough.

But Flake is one of the good guys in Washington — devoted to his conservative principles but also to the belief that lawmakers have been sent here to get stuff done. He retains strong ties to House conservatives (he’s coordinating with House Republicans to introduce the various provisions). And he predicts he can find enough Republicans to support his approach — “if we can resist the urge to shut down the government” in the meantime.

That’s a sizable if. “Make no mistake: It’s going to be tough for a lot of members to deal with this president at all,” Flake said. And Obama made clear Thursday night that the disregard is mutual. But, with luck, both sides will conclude that Flake’s plan, though imperfect, beats a poke in the eye with a sharp stick.

Twitter: @Milbank

Read more from Dana Milbank’s archive, follow him on Twitter or subscribe to his updates on Facebook.