WASHINGTON — Republican leaders moved closer on Wednesday to resolving some key differences between the House and Senate tax bills, though several big issues, including the size of the corporate tax cut, remained in flux.
As the Senate voted to begin the process of reconciling its tax bill with the House version, the Senate majority leader, Mitch McConnell, threw his support behind allowing a more generous state and local tax deduction in the final legislation.
“That sounds like a kind of reasonable idea,” Mr. McConnell said, referring to a proposal brewing among House Republicans that would give people the option of deducting up to $10,000 in income taxes or property taxes. Right now, both bills would only allow taxpayers to deduct property taxes and cap that at $10,000.
Once the conference committee process begins, lawmakers will begin formally hashing out the remaining differences, including what to do about the corporate alternative minimum tax, which crept back into the Senate bill as a late addition. The chambers are also debating how to treat the deduction that many people take for high medical expenses, a provision that is repealed by the House but expanded by the Senate.
Complicating the discussions is the need to ensure that the overall bill stays in the $1.5 trillion bucket lawmakers have budgeted for the cuts. All the changes under discussion would cost money, requiring lawmakers to find ways to offset the effect on the deficit. Lawmakers continued to debate whether to increase the corporate tax rate to 22 percent from the proposed 20 percent, an idea that President Trump appeared to support over the weekend.
Mr. McConnell publicly remains cool to the idea. On Wednesday, Representative Kevin Brady of Texas, the Republican chairman of the Ways and Means Committee, reiterated his support for a 20 percent corporate rate.
“We will take all that up in conference,” Mr. Brady said. “I continue to make the point the 20 percent rate is crucial to competitiveness.”
Mr. Brady also said that some House Republicans had called for some form of medical expense deduction to be in the final tax bill.
The conference committee, which will be made up of Republicans and Democrats from the House and Senate, will have one public meeting that is likely to take place next week. While most of the negotiations will occur behind closed doors among Republicans, Democrats will have another opportunity to publicly criticize the bill.
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.
In a sign of their confidence, Republicans are already looking past taxes to their next priority: gutting safety net programs like Medicare and Medicaid.
“We’re going to have to get back next year at entitlement reform, which is how you tackle the debt and the deficit,” the speaker of the House, Paul D. Ryan, Republican of Wisconsin, said on Wednesday during an interview with the radio host Ross Kaminsky.
During his campaign, Mr. Trump opposed cutting Medicare and Medicaid, but Mr. Ryan said that he was working to persuade him to change his mind.
“I think these reforms that we’ve been talking about, that we’re still going to keep pushing, that will help not just make Medicaid less expensive and health care itself, but it will help Medicare as well,” Mr. Ryan said during the interview. “And I think the president’s understanding choice and competition works everywhere in health care, especially in Medicare.”