Sen. Ted Cruz, R-Tex., and Rep. Alexandria Ocasio-Cortez, D-N.Y., say they agree that former members of Congress shouldn't become lobbyists, and they may be working toward a bill to stop the practice.

It's common practice in Washington that life after Congress often leads to a cushy job 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 that nearly 60% of former members from the last Congress are lobbying or influencing federal policy in some way, including former Rep. Joe Crowley, D-N.Y., whom she defeated in a 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 in a surprising cross-party show of unity.

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

"You're on."

Then, Rep. Chip Roy, R-Texas, former chief of staff for Cruz, told the duo he wanted in. Sen. Brian Schatz, D-Hawaii, agreed.

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

Craig Holman of Public Citizen called the exchange "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'd tweet back and forth with Cruz, Ocasio-Cortez had remarked on 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."