Updated 4:21 p.m. ET

President Obama is pounding Mitt Romney for his refusal to release more information about his taxes and highlighting his GOP rival's vast wealth.

Did the multiple tax returns Romney gave to John McCain factor into the Arizona senator's decision to pass over Romney as his running mate in 2008?

BLOG: Ads turn up heat on Romney's taxes

McCain told Politico today that Sarah Palin was a "better candidate" than Romney when asked if Romney's taxes were an issue. He followed up that interview with a statement that Romney would make "an outstanding president."

The Arizona senator's comments followed those by Steve Schmidt, his campaign strategist, who said Romney's wealth played a role in why the former Massachusetts governor wasn't tapped to be McCain's VP.

"We never sat around having a discussion about Mitt Romney's taxes through the prism of a liability if he were chosen" as McCain's running mate, Schmidt told The Huffington Post. The issue, he said, was that McCain had already been "caught flat-footed answering a question about how many houses he owned."

"We knew it would be a big liability that the presidential and the vice presidential candidates together owned more than a dozen homes. It was like something out of a Saturday Night Live skit. I mean, come on," Schmidt told The Huffington Post.

Romney is worth between $190 million to $250 million, according to his financial disclosure reports. He has said he will only release tax filings for 2010-2011, and has already posted on his website his return for 2010 and an estimate for last year.

Obama today is out with a new TV ad suggesting Romney is hiding something by not releasing more tax information.

In his statement, McCain said he picked Palin "because she was the best fit for my campaign, and my decision nothing to do with the bogus tax return attacks currently being waged by the Obama campaign."

A recent Gallup Poll showed 75% of registered voters say Romney's wealth doesn't make a difference to them. But 20% -- mostly Democrats and independents -- say his wealth could make a difference in how they'll vote in November.