Mr. McCarthy expressed optimism that the House and Senate would be able to bridge other gaps between the bills. House members voted Monday evening to form a conference committee that will work to resolve differences with the aim of getting final legislation to President Trump by Christmas.

In a last-minute dose of drama, the motion to go to conference unexpectedly appeared at risk of failing on Monday night because of a brewing rebellion from the conservative House Freedom Caucus over the length of a planned stopgap measure to fund the government beyond Friday.

The Freedom Caucus did not end up voting down the motion.

The proposed stopgap measure would keep the government funded through Dec. 22, requiring another spending measure to be passed just before Christmas. Representative Mark Meadows, Republican of North Carolina and the chairman of the Freedom Caucus, said there was concern about what legislation could be attached to that measure shortly before Christmas, when lawmakers would be eager to leave Washington and return home.

Instead, Mr. Meadows proposed that the stopgap spending measure stretch to Dec. 30 and warned of “bad decisions” being made in the days before the holiday.

“Having been here before, there is a rush to get home for Christmas,” he said. “In fact, there may even be a Christmas song that says, ‘I’ll be home for Christmas.’”

The House and Senate plans differ on both the number of individual tax brackets and the rates, as well as how they tax so-called pass-through businesses. They also have different international tax provisions and vary in how they treat the estate tax. The House bill fully repeals the so-called death tax, while the Senate bill raises the income threshold that determines who pays it.

The sensitivity surrounding the estate tax was on display over the weekend when Senator Charles E. Grassley, Republican of Iowa, made the case for scrapping it to The Des Moines Register. “I think not having the estate tax recognizes the people that are investing, as opposed to those that are just spending every darn penny they have, whether it’s on booze or women or movies,” Mr. Grassley said.