Nothing in the Constitution prevents a felon from being President of the United States. As for Mitt Romney, a person has to be convicted, not suspected, of committing a crime before it is a felony. Even then there’s his or her conviction is not a disqualifier for the presidency. Section 1 of Article Two of the United States Constitution sets forth the eligibility requirements for serving as president of the United States. Read it and you will never again have to invent your own qualifications for the office.
It is true that the US Constitution is silent on convicted felons running for president. The individual states make their own rules, and many of restrictions on felons running for any public office. Note that Senator Stevens of Alaska was a convicted felon when he reran for his Senate seat, but was defeated by the voters. The Senate and House ultimately decide who can be seated in Congress and who cannot.
For president, the question is largely moot. It is nearly impossible for a convicted felon to ever be elected to president because of state rules for eligibility. The question is a waste of time to even discuss.