Rep. Alexandria Ocasio-Cortez (D-N.Y.) set off a discussion Thursday on Twitter regarding possible bipartisan legislation banning lobbying by former members of Congress. (Seth Wenig/AP)

A peculiar thing happened when Congress left Washington this week: Sen. Ted Cruz (R-Tex.) and Rep. Alexandria Ocasio-Cortez (D-N.Y.) found themselves aligned and eager to work together.

Yes, that Cruz and that self-described democratic socialist known as AOC formed an alliance over Twitter on Thursday. By the end of the day, their staffs were already talking about drafting legislation together.

So what could possibly bring together two such polarizing figures in Washington?

Mutual disdain for Washington.

It’s common practice in Washington that life after Congress often leads to a cushy job on K Street lobbying former colleagues. While ethics laws forbid members of Congress from registering as lobbyists for a year (for a House member) or two (for a senator) after they leave office, the laws are loosely enforced and rife with loopholes.

Ocasio-Cortez tweeted an analysis from the watchdog group Public Citizen that found nearly 60 percent of former members from the last Congress who have taken jobs outside of politics are lobbying or influencing federal policy in some way, including Joseph Crowley, the high-ranking Democratic congressman she beat in the primary.

“I don’t think it should be legal at ALL to become a corporate lobbyist if you’ve served in Congress,” Ocasio-Cortez wrote.

Shortly thereafter, Cruz retweeted her and put in motion the most shocking political pairing in American history, or at least in recent memory.

“Here’s something I don’t say often: on this point, I AGREE with @AOC,” Cruz tweeted. “Indeed, I have long called for a LIFETIME BAN on former Members of Congress becoming lobbyists. The Swamp would hate it, but perhaps a chance for some bipartisan cooperation?”

So, Ocasio-Cortez posited this: If they could agree on a straight ban on members of Congress becoming paid lobbyists with no partisan add-ons, she would co-write the bill with him.

“@tedcruz if you’re serious about a clean bill, then I’m down,” she said. “Let’s make a deal.”

About 20 minutes later, Cruz responded: “You’re on.”

Then, just to make the bedfellowing stranger, Rep. Chip Roy (R-Tex.), former chief of staff for Cruz who most recently blocked the disaster relief aid bill, told the duo he wanted in. Sen. Brian Schatz (D-Hawaii) did, too.

Roy tweeted at Ocasio-Cortez that his staff would be reaching out to hers. “Let’s do this,” he said.

Corbin Trent, Ocasio-Cortez’s spokesman, said members of Ocasio-Cortez’s and Cruz’s staffs have been in touch about getting coffee next week when Congress is back in session. Trent said he’s been surprised at how positively people have responded to the idea of the two working together.

“People are excited at the prospect of Congress doing substantial and productive reform to what seems like corruption in D.C.,” he said. “We’re cautiously optimistic we can do something this important.”

If it comes to fruition, sometime in the future there could be a bill rollout event featuring Cruz and Ocasio-Cortez side by side.

Craig Holman of Public Citizen, whose work spurred this odd couple, called that prospect “refreshing.”

“Cruz and AOC willing to work together on revolving door abuses is quite a surprise, but it looks real,” he said. “They are talking about sponsoring legislation to impose a lifetime ban on members of Congress ever serving as paid lobbyists once they retire from public service. I don’t know how politically feasible this legislation would be, but it is a great starting point for some meaningful ethics reforms.”

Earlier Thursday, hours before she would tweet back and forth with Cruz, Ocasio-Cortez had actually remarked on the fallacies of what people think it takes to find bipartisan ground.

She shared a video of Housing and Urban Development Secretary Ben Carson saying he agreed with her that people with criminal records should be able to get housing.

“So often, bipartisanship is marketed as: a) something only ‘centrist moderates’ are capable of, or b) giving up your principles to ’get things done’,” Ocasio-Cortez tweeted. “I couldn’t disagree more. You don’t have to abandon your principles to agree. Being curious about other people’s values helps, too.”