It's ironic that a discussion of the public's comfort-level with Mormons should be pegged to a question about politicians, since The Church of Jesus Christ of Latter-day Saints is meticulously neutral in partisan politics.
Actually, the Church may be making good ground, if a Washington Post report less than two weeks ago can be relied upon. Neither can I accept the gross overstatement that suspicions "plague" Mormon politicians, as the question claims. That would be news indeed to the 15 elected members of the current Congress for whom their church affiliation has never been a barrier for them or their diverse constituents.
In reality, Americans don't look to high-profile politicians, such as Majority Leader Harry Reid, or to former governors Mitt Romney and Jon Huntsman Jr., to understand our faith. Neither do they look to personalities like Glenn Beck, who touches on his faith occasionally but who doesn't claim to speak for the Church or other members. I suggest that people are much more likely to dismiss stereotypes after associating personally with their Mormon neighbors or colleagues at work - the people they know best.