Washington (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."

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