"I think it's always good when the president is talking to both sides," the Republican congressman from California said in an interview on CNBC's "Squawk Box."
On Wednesday night, top congressional Democrats said they reached a deal with Trump on the Deferred Action for Childhood Arrivals program, which shielded certain immigrants brought to the U.S. as children. The president on Thursday morning denied a deal had been reached but said they were close.
This latest bipartisan outreach came after Trump split with Republicans and worked with Democrats last week on a short-term debt ceiling extension that included a package to approve relief funding for Hurricane Harvey.
Asked whether House Speaker Paul Ryan or Senate Majority Leader Mitch McConnell were angry that Trump went around them on DACA and the debt ceiling, McCarthy said: "I don't think people are miffed if we're able to get something done here."
McCarthy also agreed with the president and said DACA "needs to be fixed as we move forward."
"I would like to see immigration overhauled completely because I think it's crazy we have individuals come to America, become engineers and you tell them to ship them someplace else," McCarthy said.
"I don't think this country is going to move these individuals out," he added. "This is the only country they have known."
Regarding tax reform, McCarthy says the U.S. corporate tax rate is one of the highest in the world and it must be fixed.
"We know we have to be in the range of 25 percent or lower all down to 15," he said. "The lower we go, the more competitive we are around the world."