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 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 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."
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, 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 pro choice to pro-life has helped keep alive former Sen. Ted Kennedy's zinger that Romney's "multiple choice" over abortion. Some Christians are queasy about his Mormon faith. And Romney's health care 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.
Yet Romney has somehow avoided sharp, prolonged exchanges over "RomneyCare." But then former Pennsylvania Sen. Rick Santorum, the primary race's attack dog, started chewing away at Romney for having "no credibility." He kept interrupting.
And for the first time, it happened — Romney looked unsettled.
"Why don't you let me speak. Rick, you had your chance, let me speak," Romney said.
Newt Gingrich chimed in and criticized Romney's health plan. Romney then pointed out the idea for an individual mandate in his health plan came from Gingrich and the conservative Heritage Foundation.
"Have you supported in the past an individual mandate?" Romney asked.
Said Gingrich: "I absolutely did."
The winner of that exchange could be Obama, who largely escaped being bashed as the Republicans went at each other.
It was then Perry's turn to fluster Romney. Slipping a question about the high rate of the uninsured in Texas, Perry pointed out that a company called Community Lawn Service with a Heart employed illegal immigrants who worked at Romney's house in 2007.
"You hired illegals in your home and you knew about it for a year," said Perry, who has been blasted for supporting in-state college tuition rates for some illegal immigrants. "And the idea that you stand here before us and talk about your strong record on immigration is on its face the height of hypocrisy."
Romney started to deny hiring the immigrants — who were interviewed by reporters at the Boston Globe — but Perry kept interrupting him.
"Are you going to let me finish?" Romney asked, chiding Perry for his poor debate performances in the past. "It's been a tough couple of debates for Rick and I understand that," Romney said. "And so you're going to get testy.'
The pro-Romney crowd cheered.
Then it was Cain's turn. He was asked to explain his call for an electrified fence across the border with Mexico. Cain said over the weekend he was joking, but on Tuesday he said he supported the idea.
Later in the debate, Cain had a complicated answer to a question about whether he would have authorized a hostage swap with a terrorist group. He said he wouldn't. But he also had said that he could see approving a prisoner exchange similar to the one between Israel and Hamas, which has been branded a terrorist organization.
The nuanced — critics say contradictory — responses to the hostage negotiations highlight one of Cain's major weaknesses: foreign policy. Coupled with his refusal to give specifics about his 9-9-9 plan, Cain is in danger of meeting the same fate as Perry and Bachmann: He's not living up to expectations, and he's not growing as a candidate during the debates.
The Iowa caucus is Jan. 3 and the Florida primary is Jan. 31. The other three early vote states lie somewhere in between. It takes money and organization to help ensure wins there. Cain doesn't have much of either (nor does Bachmann, Gingrich or Santorum). Perry does. Romney has it in spades. Wild-card candidate Ron Paul, who has one of the most dedicated followings, could stick around and became a major factor in the months ahead.
In one pointed question, Cooper asked Cain who should be president; Perry or Romney?
"No," Cain said. "I should be president."
So not Mitt Romney. Or is it Not Mitt Romney?