An undivided government could pave the path for repealing President Barack Obama's health care reform and engaging in a big infrastructure program, Cantor said. But it comes after many Republicans in Washington declined to support Trump's presidential bid.
Despite differences with Trump, Cantor predicted that Paul Ryan will stay as House speaker.
"Where [Trump] will have to work is bringing along House Republicans, who insist that any additional spending be paid for," the former Virginia congressman said. "In my opinion, the only way they're going to find the money to pay for that is through tax reform, and through ... repatriation on the international front. There'll be a lot of struggle, but I do think there's going to be some progress made."
Democrat George Mitchell told "Squawk Box that partisanship neither began nor ended with this campaign.
He said Trump would be smart to start by focusing on infrastructure, an area where liberals also support investment. Repatriation of funds held overseas could also be an olive branch between the two major political parties, the former Senate majority leader from Maine said.
"A democracy requires an effective opposition to present alternatives to the administration to seek common ground where it does exist," Mitchell said.