Cantor to GOP: Don't ‘relitigate’ Obama presidency

New Congress, old battles?

Former House Majority Leader Eric Cantor called on President Barack Obama and congressional Republicans to get something done and avoid "relitigating" well-defined differences that have been hashed out over the last six years.

The Republican former congressman said the president has an opportunity to implement a pro-growth policy by supporting the Trade Promotion Authority—a legislative procedure through which Congress defines U.S. negotiating objectives. Obama must also stand up to critics of free trade such as Massachusetts Democratic Sen. Elizabeth Warren, Cantor said in an interview Tuesday on CNBC's "Squawk Box."

Meanwhile, Republicans must dispense with differences on immigration and deal with funding the Department of Homeland Security, he added. Congress voted in December to fund the agency only through the end of February.

Read MoreCantor: Here's what Congress needs to do in 2015

"The president's got to able to stand up to his side, and some would allege the extremes on his side, and the Republican leadership as well is going to have to deal with some of those who want to employ tactics that are somewhat extreme that could lead to a government shutdown, a department shutdown, or something like that," Cantor said.

The low expectation mark for grading this Congress will be whether it can avoid brinkmanship, he said.

Cantor was interviewed hours before the GOP-led 114th Congress was to be sworn in.

Cantor, a seven-term Republican congressman from Virginia, lost his GOP primary race in June to David Brat, a tea party-affiliated economics professor. Cantor is now vice chairman and managing director at boutique investment banking firm Moelis & Co.