Sen. John McCain (R-Ariz.) told Fox News Channel’s Neil Cavuto on Tuesday that he thinks House Speaker John Boehner (R-Ohio) and Senate Minority Leader Mitch McConnell (R-Ky.) should tap freshman Sen. Rob Portman (R-Ohio) to sit on the bipartisan 12-member committee that will be formed as part of the debt-limit agreement.

“One of my candidates – maybe I shouldn’t say it; I’m not making the decisions — but one of my candidates would be Rob Portman, former head of OMB,” McCain said. “A very sober, knowledgeable person. I think those are the kind of people that are going to be on this committee.”

A Portman spokesman declined to comment Tuesday.

Portman, a former six-term House member, U.S. trade representative and Office of Management and Budget director, is seen as a rising star within the Senate Republican conference. He has worked closely with McConnell during the debt-limit battle.

The decisions on who gets to serve on the bipartisan panel will ultimately be made by top party leaders in each chamber. McConnell and Boehner will choose three Senate Republicans and three House Republicans, while Senate Majority Leader Harry Reid (D-Nev.) and House Minority Leader Nancy Pelosi (D-Calif.) will select three House and three Senate Democrats.

But McCain’s remarks Tuesday mark the first of what’s likely to be many instances of members weighing in on their preferences for the panel. Senate leaders, asked repeatedly by reporters over the past several days who they might pick, have declined to say.

One option is for members of the Gang of Six to sit on the panel. The bipartisan group of senators has made significant progress toward a comprehensive deficit-reduction plan. So far, the gang’s members have declined to say whether they’re eyeing seats on the panel.

“It’s presumptuous of me to say anything about the make-up of the committee,” Sen. Kent Conrad (D-N.D.), the Senate Budget Committee chairman and one of three Democrats in the Gang of Six, said Sunday when asked whether he’d like to sit on the committee.

Sen. Mike Crapo (R-Idaho) also declined to say whether he’d like to take part in the committee, but said that the group “certainly could” use the work already done by the Gang of Six as a starting point.

“I mean, look, the Gang of Six has done the work,” Crapo said in a brief interview Sunday. “So one way or the other, if you truly approach a comprehensive shift in American fiscal policy, this is in my opinion the most powerful proposal out there on the table, and I would hope that it would get very strong consideration.”

Still, some members of both parties’ bases have expressed opposition to the Gang of Six plan; some Democrats believe the cuts it would make are too deep, while a key sticking point among Republicans has been the inclusion of tax increases as part of a comprehensive deficit-reduction plan.

Asked Tuesday about Obama’s insistence that tax increases be included as part of a “balanced deal,” McCain dismissed the idea.

“Hello? He just wants to spend more money,” he told FNC’s Cavuto.