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(CNN) —  

Two more Republicans signed on to a measure that would force an immigration vote in the House just hours after Speaker Paul Ryan urged his colleagues not to in a closed-door meeting Wednesday.

The momentum of the petition, paired with threats from conservatives to cause problems if the effort continues to move, prompted House leadership to summon both key moderate and conservative members to meet in Ryan’s offices with the full GOP leadership team Wednesday evening. But the issue remained far from resolved.

The signatures of New York Rep. John Katko and Michigan Rep. David Trott on Wednesday brought the total to 20 Republicans supporting the move, five short of the number needed to force a vote if all Democrats sign on as well.

The pitch from Ryan to his party colleagues at a meeting that morning as well as the evening huddles, as recounted by multiple lawmakers leaving the meeting, came as he faces an uprising from moderate GOP members who say time is running out for him to come up with a solution on immigration, adding they are tired of waiting for action.

Texas Rep. Bill Flores paraphrased the speaker as telling Republicans in the morning to “quit messing around with the discharge petition” and that it’s “not a path to success.”

“He just said a discharge petition is not a path to success if you really want to do something on immigration,” Flores told reporters.

Majority Leader Kevin McCarthy also weighed in. A source familiar with his remarks said McCarthy was quite serious in warning the conference about the effects the discharge petition could have on the midterms. Florida Republican Rep. Carlos Curbelo said he didn’t explicitly say the effort could threaten the House majority but did say “that it’s important for us to work as a team.”

Other members and Flores said Ryan told his colleagues that he met with President Donald Trump the day before and that leadership and the White House were working on a plan that could ultimately pass both chambers of Congress and get the President’s signature. But he did not offer specifics, the lawmakers added.

A group of moderate Republicans are backing a plan to bypass GOP leaders by forcing a floor vote on four competing bills to preserve the Obama-era DACA program, which protected young undocumented immigrants who came to the US as children. Trump has decided to end the program, though it’s currently tied up in the courts.

The move, called a discharge petition, now has 20 Republican supporters. When Katko and Trott signed during the first vote series of the day – which is the main opportunity that lawmakers have to sign by hand the petition kept on the House floor – Republican petition backers, California’s Jeff Denham and Curbelo, were seen walking the floor, talking to members and each other.

Both moderates and conservatives leaving the speaker’s offices in the evening said they had “productive” and good meetings, which included the top five House Republicans including Ryan, McCarthy and Whip Steve Scalise of Louisiana.

But both also insisted that nothing in the meetings changed their efforts. Moderates are still pursuing the discharge petition and conservatives are still threatening an unrelated farm bill to push for their preferred immigration bill, a hardline measure that lacks the votes to pass the House.

Moderates included Reps. Denham; Curbelo; David Valdeo, R-California; Fred Upton, R-Michigan; and Will Hurd, R-Texas. Florida Rep. Mario Diaz-Balart stopped by but couldn’t stay because he had committee obligations.

The conservatives meeting were Freedom Caucus Members Reps. Mark Meadows, R-North Carolina; Jim Jordan, R-Ohio; and Scott Perry, R-Pennsylvania.

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“It was a conversation, I’m not going to divulge all the details … but it was productive,” Curbelo said. “Clearly we have had a positive impact on our leadership and this institution because now this issue is being taken seriously and people are thinking through how something can be achieved.”

“The next step is figuring out what the next step is,” Meadows said.

Leadership called the meetings, members said.

“The meeting was prompted when we got number 20 today