One additional Republican signed the petition Wednesday, Rep. Erik Paulsen of Minnesota. Four more GOP signatures are necessary, should all 193 Democrats sign.

The proponents had informally aimed to complete the petition by Thursday, when Congress is set to leave Washington for a week-long recess, which would force votes on June 25 — one of a limited number of days this year when discharged measures can be considered under House rules.

But a Democrat who is working closely with the Republicans leading the effort said GOP leaders had succeeded in slowing down the push.

“It’s become tougher,” said Rep. Pete Aguilar (D-Calif.). “We continue to be optimistic that we’ll get there, but it’s hard — it’s hard to get to 25 or 26 [Republicans]. … Leadership’s working them to try to keep them from signing.”