Each party in each chamber of Congress gets three spots, but it's highly unlikely that the leaders would tap someone facing a tough 2012 election fight.
"I don't particularly want to be on the committee," said Hatch, who opposed the debt deal. "I don't expect to be on it because tax revenues are going to be in play, and I can't vote for increased taxes."
Stephen Hess, a congressional scholar at the Brookings Institution, wonders who really does want one of the 12 spots.
"It is a consuming job, besides being a controversial job," he said. "You are a patriot if you take this position."
The supercommittee must come up with a plan by Thanksgiving, then Congress must vote before Christmas. Under the debt deal passed Tuesday, the House and Senate can't amend what the supercommittee comes up with or block it from a vote.
If the committee fails or Congress rejects its plan, the government would face automatic budget cuts equal to $1.2 trillion, with 50 percent coming out of domestic programs and 50 percent out of defense spending. That's something both parties find unpalatable, which should spur them to find a compromise.
President Barack Obama has made it clear that he wants the supercommittee to raise taxes on the wealthy, which he tried but failed to obtain in the bill that increased the nation's borrowing amount. Republicans will try to block those plans and instead take bigger chunks out of domestic programs while reducing the impact on the military.
Hess said in this environment, the committee is likely to frustrate just about everybody and that's a tough spot to be in when you are running an aggressive re-election campaign.
Hatch has already amassed more than $3.4 million in his campaign account and hired more than 25 staffers as he seeks to block a potential challenge from his right, spurred by upset tea party Republicans. Rep. Jason Chaffetz, R-Utah, and state Sen. Dan Liljenquist are likely challengers.
Without that pressure, Hess said, Hatch has the right experience and stature to be among the three senators selected by Senate Minority Leader Mitch McConnell.
"He is a very logical choice. Ordinarily, he would do something like this, but my hunch is that Mitch McConnell protects him," said Hess. "He's aware that Orrin Hatch is being challenged."
But backing away from the supercommittee's work could also undermine one of Hatch's campaign themes. He's been telling voters that his six terms in office has him uniquely placed to revamp the tax code and remake Medicare.
Hatch isn't concerned, saying he expects the members of the supercommittee to ask him and others on the Finance panel to provide a set of options, since they are the senators who know the most about this area.
"I know a lot of this work will come to the Finance Committee anyway," he said.
Former Sen. Bob Bennett was one of McConnell's closest advisers in past years and Bennett expects his friend to select his three picks for the supercommittee without regard to seniority or current committee assignments, the two criteria that make Hatch a likely candidate.
"To make a sports analogy, he would say: 'Let's go with the best athletes rather than those who have been on the team the longest,' " Bennett said.
Bennett faced a similar situation during the negotiations for the Troubled Asset Relief Program (TARP), also known as the Wall Street bailout. He was the top Republican in the meetings, but McConnell asked former Sen. Judd Gregg to take the lead on the details.
Bennett lost his re-election bid in 2010 in part because of his role on TARP. Tea-party favorite Mike Lee won the seat.
Bennett suggested that this time McConnell is likely to go with trusted allies and aggressive negotiators facing little political pressure, such as Sen. Jon Kyl, R-Arizona, who has already said he won't seek another term, or Sen. Lamar Alexander, R-Tenn., whom McConnell relied on during past health care negotiations.