(CNN) Democratic Rep. Alexandria Ocasio-Cortez and GOP Sen. Ted Cruz came together Thursday on Twitter in a professed effort to ban former lawmakers from taking paid lobbying positions.

In an ambitious bipartisan effort, the two seemingly opposite legislators found common ground in their disapproval of former members of Congress wielding their influence in new careers as government lobbyists.

Ocasio-Cortez kicked things off, tweeting, "If you are a member of Congress + leave, you shouldn't be allowed to turn right around&leverage your service for a lobbyist check."

"I don't think it should be legal at ALL to become a corporate lobbyist if you've served in Congress," she added. "At minimum there should be a long wait period."

Cruz then retweeted the New York Democrat's statement, saying he agreed with her, adding that "the Swamp would hate it."

"Here's something I don't say often: on this point, I AGREE with @AOC," he 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?"

Ocasio-Cortez told the Texas Republican that if the bill pertained only to lobbying, she would spearhead the effort with him.

".@tedcruz if you're serious about a clean bill, then I'm down. Let's make a deal," she tweeted. "If we can agree on a bill with no partisan snuck-in clauses, no poison pills, etc - just a straight, clean ban on members of Congress becoming paid lobbyists - then I'll co-lead the bill with you."

Cruz replied, "You're on."

Soon afterward, Republican Rep. Chip Roy of Texas and Democratic Sen. Brian Schatz of Hawaii -- potential bipartisan sponsors for legislation in both chambers of Congress -- chimed in.

"Happy to lead or otherwise co-sponsor in the House, @AOC and @tedcruz," Roy tweeted, adding that his staff was reaching out to hers. "Let's do this."

Schatz tweeted simply, "IN."

Ocasio-Cortez pointed to the quick responses as a sign of more sponsors to come.

"And that's just in a few hours - there will surely be more from both parties to sign on. Nice," she tweeted.

CNN has reached out to the offices of Ocasio-Cortez, Cruz, Roy and Schatz for comment.

The lawmakers' decision to join forces strays from their usual partisan clashes, as Cruz has gone after Ocasio-Cortez in the past. The senator has criticized the Green New Deal, Ocasio-Cortez's proposed plan to combat climate change, as "extreme" and mocked it for getting "ZERO votes."

Their last Twitter feud, however, focused on something even more unique than policy -- croissants.

In April, Ocasio-Cortez lamented how "croissants at LaGuardia are going for SEVEN DOLLARS A PIECE...Yet some people think getting a whole hour of personal, dedicated human labor for $15 is too expensive??"

Cruz responded with a jab at the congresswoman's socialist leanings, tweeting, "Oh the humanity! Here's the answer: government-mandated FREE CROISSANTS FOR ALL. And we'll just force the bakers to give all of their time for free. #SocialistLogic #AprilFools"

Ocasio-Cortez seemed to address Cruz in her general retort accusing her Republican critics of missing her point.

"GOP taking every tweet so earnestly, making my point for me. It's not an argument against the price of a croissant - it's about the value of human worth," she tweeted. "But I guess that idea is foreign to them since their policies treat people as disposable anyway."