House Majority Leader Kevin McCarthy said Monday the Senate passage of the tax bill on schedule proves the overhaul can be done this year.
"It happened on the timeline we said it would, McCarthy said in an interview with CNBC's "Squawk Box."
The Senate and House must now reconcile their versions of the legislation. The House passed its bill last month.
"There are differences in this bill, but there are not that great of differences," McCarthy said. "We can work and have it done this year."
"I'd like to do it faster," McCarthy added.
McCarthy said he credits Trump and Senate GOP leadership for passage. The president "put a lot of time and effort in," the California Republican said.
Trump praised the Senate for passing "tremendous tax reform" and said, "people are going to be very, very happy." On Monday, Trump said on Twitter the passage could be "big day for the Stock Market - and YOU!"
@realDonaldTrump: With the great vote on Cutting Taxes, this could be a big day for the Stock Market - and YOU!
On changes to individual income tax brackets in the Senate and House versions, McCarthy said, "I think we can work that out. ... I would actually like to see the rates go even lower, if possible." The House bill proposes four tax brackets while the Senate would keep seven.
"I don't think anybody should be punished for being successful," he added. "I worry about deficit, but you're not going to get out of this problem until you grow the economy."
— Reuters contributed to this report.