“I have no doubt in my mind that if it passes the Senate — in something close to what it’s like now — that it will pass the House,” said Rep. Tom MacArthur (R-N.J.), a moderate who negotiated portions of the bill that passed the House in early May.

His conservative counterpart, Rep. Mark Meadows (R-N.C.), called the latest Senate version “a step in the right direction” and suggested it would “have to be a big move” away from the current draft to sink the bill in the House. Either way, he said, conservatives will not object if House Speaker Paul D. Ryan (R-Wis.) takes the Senate bill and places it on the House floor in a take-it-or-leave-it moment.

“I realize the reality is, we’re not going to change it when it comes back here,” said Meadows, chairman of the House Freedom Caucus, the most conservative group in Congress.