Republicans should pursue a "more traditional" approach to corporate tax reform that does not include the House's border adjustment import tax provision, Sen. Rob Portman told CNBC on Wednesday.

Portman, director of the Office of Management and Budget under President George W. Bush, said on "Squawk Box" he understands some of the economic reasons for the border tax. But he advocates "simplifying the darn thing" by building consensus around conventional means of providing relief to businesses such as lowering the rates and broadening the base.

The House GOP plan on corporate tax reforms looks to lower the federal rate from 35 percent to 20 percent, with the border tax provision helping pay for the entire package.

President Donald Trump has expressed a desire to lower the corporate tax rate, but the White House has been vague on whether there's support for the border tax proposal.

Portman, who had been discussed during the campaign as a possible vice presidential pick for Trump, predicted taxes would indeed by the priority after the failure of the House GOP Obamacare replacement bill.

Portman did say Obamacare cannot be left in place because of rising premiums and lack of chance. "We can't give it up because right now the status quo is unacceptable to everybody," he said. But health care reform has to wait until after taxes, he predicted.

