Give me some help here, I can’t think of any so far.
crickets
“Will everybody please drop it about the Massachusetts health-care plan? When I signed it, I was totally shitfaced on Jack Daniels.”
“I’m gay” ?
“The LDS Church is wrong about everything” ?
“I hate my wife” ?
“One time in band camp…”
Well, this quickly devolved into a joke thread… or maybe it was intended to be?
But if we take it as a serious question, I guess what is being asked is: what politically popular position would Romney not take due to principled objection.
My first thought was immigration, but he pretty significantly moderated his immigration position at the last debate. Tax cuts for the rich are unpopular, but he pretty clearly stated that he will not cut taxes for the top 10%. He obviously moderated (twice) on abortion, and move right-ward on same-sex marriage.
Hm…
I guess the one thing he still refuses to say (that would be politically popular, I think) is: “I’m willing to trade small tax increases for large spending cuts.”
Support for gay marriage - that’s a fairly popular stance right now and he’s visibly losing celebrity support due to his stance, but I haven’t seen him flip that one yet.
On a less serious note - support for polygamy! Because Ann just isn’t enough!
“I strongly support human rights both at home and abroad. To that end, if elected, I intend to repeal the Patriot Act, scale back the War on Drugs, move the focus of our criminal justice system from punishment to rehabilitation, bring all of our troops home from foreign bases around the world, and cease having friendly diplomatic relations with notorious human rights abusers such as China.”
I feel pretty %&$# sure that he’ll never say that.
It could go either way. I think it’s turning out OK so far.
He won’t answer any “boxers or briefs” questions for some reason.
The only thing I can’t imagine him saying is “I don’t want to be president.”
– I’m not going to give America up.
– I’m not going to let America down.
I don’t think he’d ever say “Mormonism is a cult!”
He hasn’t converted to protestantism even thought that would help his election chances.
He’s been pretty much unwavering in his desire to roll back government regulations, (although he hasn’t been very specific.)
Near as I can tell he has a Norquest level aversion to raising taxes. However his derision of the 47% indicates that he would favor reducing the number of people who pay no taxes, and so effectively raising taxes on the lower classes.
The truth; in like. “My wife wasn’t really a working mom, she was a rich mom with a staff. It’s not like managing a staff that takes care of your kids is a traditional working mom job. I’m trying out this honesty thing for size and have deep commitments to it now; believe me, so now please elect me.” 
But that is just because it would hurt his chances to get elected. If being an out of touch plutocrat was what America wanted in a president I’m sure he would have be glad to display his credentials. The question is are there any stances that he wouldn’t take that might help him get elected.
But to support your point, even if it would help him get elected I don’t think he would dispose of the vast majority of his worldly goods and live on $50,000 a year.
He’s also taken a firm stand in the area of not revealing his tax forms.
Apparently he won’t say that 60% of the jobs Obama created have been low-paying ones, and about as many lost over the past 4 years were mid-pay jobs.
“From each according to his ability, to each according to his need”.
“If elected, I promise to legalize marijuana.”
“You know, this Joseph Smith guy was kind of a kook.”
“Black power!”