Rep. Alexandria Ocasio-Cortez and Sen. Ted Cruz’s bipartisan Twitter pledge Thursday to work on a measure preventing former lawmakers from becoming lobbyists has picked up Democrat Sen. Brian Schatz and Republican Rep. Chip Roy.

The motion started when Ms. Ocasio-Cortez, New York Democrat, tweeted: “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.”

Texas Republican Mr. Cruz joined in, saying he supported a lifetime ban and suggest the two work on a resolution together.

“The Swamp would hate it,” he tweeted.

Ms. Ocasio-Cortez said as long as the bill was “clean” she would co-lead a bill with Mr. Cruz.

In response, Hawaii Democrat Mr. Schatz simply wrote “IN.” while Mr. Roy, a Texas Republican, said he would either “lead or otherwise co-sponsor” the bill as well.

Ms. Ocasio-Cortez tweeted: “Okay, with [Mr. Schatz] + [Mr. Cruz] we’ve got at least one D-R team in the Senate to ban members becoming lobbyists, & myself w/ [Mr. Roy] makes at least one D-R team in the House. And that’s just in a few hours - there will surely be more from both parties to sign on. Nice.”

In response, presidential candidate Michael Bennet pledged his support in a Twitter video, adding it’s a bill he’s had “for 10 years.”

“This is a bill that I had forever and I couldn’t find a single co-sponsor because everyone wanted to become a lobbyist,” he said. “Now Ted and AOC to the same idea and that’s great. We should ban members of Congress from every becoming lobbyists.”

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