If the Republican presidential race were a logic problem, there would be just two candidates:

1)      Mitt Romney

2)      Not Mitt Romney 

And that’s bad news for Herman Cain.

Ask Rick Perry. And before him, Michele Bachmann. Each candidate once held the Not Mitt Romney mantle — that is, a reasonable claim to near-frontrunner status — only to wind up at the back of the pack.

After Tuesday night’s verbal brawl of a debate in Las Vegas, it’s a good bet that Cain could meet a similar fate. Perry could rise after a stronger-than-usual debate performance in which he savaged Romney for hiring a home lawn service that employed illegal immigrants.

The attack flustered the normally unflappable Romney. The sharp exchange dominated Twitter, blogs and the after-action talk of the pundits. And that robbed Cain of some of the spotlight.

Heading into the debate, Cain was fighting a rearguard action over his “9-9-9” plan that would cut corporate and personal income tax rates to 9 percent while raising a first-ever national sales tax of 9 percent. 

Business groups and other Republicans have called the sales tax a job killer. An independent study shows that the plan would give millionaires a savings of at least $455,000, while raising tax expenditures for poor and middle-income people. Everyone would have to pay the new national sales tax on top of state sales taxes.

Cain said critics were confused about his plan, mixing up “apples and oranges.”

Romney then hijacked the debate from CNN’s Anderson Cooper by breaking the rules when he asked a question directly of Cain.

“Are you saying that the state sales tax will also go away?” Romney asked.

“No, that’s an apple. We’re replacing a bunch of oranges,” Cain responded, drawing laughs from the crowd.

“Will the people in Nevada not have to pay a Nevada sales tax and [instead] pay a national sales tax?” Romney asked.

“No,” said Cain. “You’re going to pay the state sales tax no matter what.”

Said Romney: “I’m going to be getting a bushel basket that has apples and oranges in it because I’ve got to pay both taxes.”

Big laughs.

Throughout the eight GOP debates, this has been Romney’s fate: He has charmed the crowd while the Not Mitt Romney has borne the brunt of the attack. Romney’s poll numbers have climbed from about a fifth of the GOP vote to almost a third in some surveys.

But Romney can’t seal it up. Many conservatives just don’t trust him enough. So they’ve been searching for more candidates like serial daters.

But Romney can’t seal it up, with a Wednesday NBC poll showing he and Cain were virtually tied at roughly 30 percent of the vote in Florida; Perry was at 8 percent. Many conservatives just don’t trust him enough.

So, like serial daters, they’ve been searching for more candidates. Romney’s relative primary weakness – his perceived moderation – is his strength in a general election, where he would fare best against the president, according to most polls.

Romney’s shift from being pro-choice to pro-life has helped keep alive former Sen. Ted Kennedy’s zinger that Romney is “multiple choice” on abortion. Some Christians are queasy about his Mormon faith. And Romney’s healthcare plan from his days as Massachusetts governor was a template for President Barack Obama’s health plan, which is reviled by conservatives nowadays because it has a government mandate requiring individuals to purchase health insurance.