Republican lawmakers are looking to quickly resolve differences so they can get the bill signed and to Mr. Trump by Christmas.

“I can’t imagine having come this far we’re not going to finish the job,” Mr. McConnell of Kentucky told the radio host Hugh Hewitt on Wednesday. He added that he was “almost certain” that the bill would reach the desk of Mr. Trump.

Mr. Trump, for his part, expressed optimism on Wednesday that the bill would get to him quickly and said that he expected the tax bill to help drive a surge in economic growth to 6 percent — a level far greater than most economists believe possible.

“So we’re at 3.3 percent G.D.P.,” Mr. Trump said, referring to gross domestic product, a measure of the economy’s strength. “I see no reason why we don’t go to 4, 5 and even 6 percent.”

Mr. Trump said that there were parts of the Senate and House bills that he preferred but that he was confident the final version would be better than both proposals. He said that the last step of the process would ensure that the “sliver” of taxpayers who do not currently receive relief from the legislation were taken care of.

On Wednesday night, Senate Republicans announced that Orrin G. Hatch of Utah, Mike Enzi of Wyoming, Lisa Murkowski of Alaska, John Cornyn of Texas, John Thune of South Dakota, Rob Portman of Ohio, Tim Scott of South Carolina and Pat Toomey of Pennsylvania would sit on the conference committee.

In a sign of their confidence, Republicans are already looking past taxes to their next priority: gutting safety net programs like Medicare and Medicaid.