(CNN) Rep. Alexandria Ocasio-Cortez says a ban on former lawmakers becoming lobbyists, which prompted her unlikely alliance with Sen. Ted Cruz, is one step closer to becoming a reality.

"Our legislative teams are meeting, so we're going to see how far we can push this," the New York Democrat told The Young Turks in an interview published Thursday.

"The real key here, though, is in the loopholes," Ocasio-Cortez said Thursday, arguing that some former members of Congress get around lobbying registration requirements by consulting lobbying firms externally.

"So the real question here that we're trying to figure out in this collaboration is how far he's willing to go," she said of Cruz. "Is this just about the letter of the law or is he serious about really banning lobbying in spirit? And so I'm really looking forward to seeing where and how far they'd be willing to move on that, but I'm encouraged."

Cruz's press secretary Maria Jeffrey told CNN in a statement Friday, "Our teams are in talks and we are hopeful to find a legislative solution to what Senator Cruz and the Congresswoman agreed to on Twitter, which is a clean bill that would prohibit former members of Congress from lobbying."

Ocasio-Cortez also said that Republican Rep. Chip Roy of Texas -- Cruz's former chief of staff -- "reached out to us as well" on the measure, but she did not elaborate on the extent of their collaboration.

The congresswoman called working with Cruz "really weird," but maintained that her commitment to "swallow all of my distaste in this situation" showed true bipartisanship.

"It's super bizarre. Really weird. Never thought in my life that one of my first pushes would be alongside Ted Cruz," she said.

"It really shows what the true spirit of not being partisan is, in that bipartisanship doesn't mean, let's come together to go to war and lower taxes on the rich," she continued. "But bipartisanship means, OK, I will swallow all of my distaste in this situation because we have found a common interest. And common cause, I think, can transcend bipartisanship, and I think that's the way that we should go."

The two lawmakers showed similar shock at the situation when they initially joined forces on Twitter.

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 her statement, saying he agreed with the New York freshman.

"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 said that if Cruz was "serious about a clean bill, then I'm down" to co-lead it.

"You're on," Cruz responded, with Roy and Democratic Sen. Brian Schatz of Hawaii -- potential bipartisan sponsors for legislation in both chambers of Congress -- also offering their support.

While the exchange may have seemed unusual for the seemingly opposite lawmakers, so did their previous Twitter exchange -- a feud over croissants.

In April, Ocasio-Cortez lamented that "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"

This story has been updated to include comment from Cruz's office.