When the bipartisan mavericks betrayed Senate Majority Leader Bill Frist (R-Tenn.), many pundits wrote off the presidential prospects of both Dr. Frist and his nemesis, Sen. John McCain (R-Ariz.).

Frist looked weak and ineffective, the insiders reasoned. And they predicted that McCain’s actions had finally and forever alienated him from influential conservatives, ruining his Republican nomination prospects.

Both those conclusions are dead wrong in my view. The judicial-nomination compromise episode may ultimately push both Frist and McCain to the forefront of the 2008 presidential competition.

Frist will be hurt least by the whole episode. It may even enhance his prospects by causing some of his opponents to underestimate his potential strength as a presidential candidate.

Washington insiders seem to assume, quite wrongly, that a candidate’s presidential timber is measured by his congressional leadership skills. If that were true, wouldn’t Bob Dole or Dick Gephardt have become president?

No, success in the House or Senate has almost nothing to do with winning the White House. In fact, the electorate’s current (and long-standing) antipathy regarding Congress might actually make success on Capitol Hill somewhat of a liability.

I can see the proclamations now: “In Congress, Larry went along so he could get along. Now Larry will be a great president! Elect Larry to lead our nation like he led Congress.”

The core of Frist’s appeal has always been, and will always be, the mystical quality of his being a physician, a healer. He’s not just a regular doctor, either. He’s a heart surgeon who has thrust his hands into people’s chests to lay hold of their life-giving organ and rescue their very lives.

Here’s an idea for a new reality TV show that merges “American Idol” with “Family Feud.” Let some of Frist’s former patients talk for 10 minutes about the good doctor, what he meant to their families and what he could mean to America. Then we let a panel of smart Washington insiders wearing suits — say Tucker Carlson, Chris Matthews and George Stephanopoulos — drone on about Frist’s “weak and ineffective” Senate leadership and how America would suffer if he were to lead us from the White House. Then we’d let America vote. Frist would whack Washington’s best.

Maverick McCain’s situation after the latest judicial-nominee compromise is more complex. The term “maverick” evolved in Texas. A signer of the Texas Declaration of Independence, Samuel Augustus Maverick, refused to brand cattle on his sprawling ranch. Unbranded calves everywhere started being referred to as “mavericks.” Somewhere along the way, the label was generalized to any sort of nonconformist.

But it’s the original meaning that’s relevant today. McCain doesn’t wear anyone’s brand, especially not a party brand. He may still belong to the Republicans, just as Sam Maverick’s cattle were his property, but without a brand McCain can roam around a bit.

Mavericks address the core complaints expressed by ordinary voters about Capitol Hill. In focus groups, voters attack Washington’s mentality of “I’ll scratch your back if you scratch mine.” They also believe that most members are co-opted by a system that forces congressmen to abandon their constituencies and core beliefs in exchange for acceptance by the establishment. So voters respond positively to anyone authentic, anyone who appears to resist branding.

I once asked voters in a Florida poll to rate the appeal of a “maverick who sometimes crosses party lines to vote for what he thinks is right rather than what his party wants him to do.” Two-thirds (67 percent) of the voters interviewed said such a candidate would be “very appealing.” Virtually every Republican and Democrat constituency was equally enthusiastic. Only weekly churchgoers and self-described “very conservative” voters slacked in enthusiasm for the maverick. But a majority of even those groups found the maverick very appealing.

Many Republicans feel McCain’s maverick streak bears witness to the man’s authenticity. That perceived authenticity could attract supporters, even from among the ranks of Republicans who disapprove of some of the senator’s policies.

Hill is director of Hill Research Consultants, a Texas-based firm that has polled for GOP candidates and causes since 1988.