Here’s something top Democrats are watching closely: Will there come a point when all the media coverage of the turmoil inside Mitt Romney’s campaign — combined with his mismanaged convention and trip abroad — seriously undermine one of his core strengths, i.e., his “Mr. Fix-It” aura?

The media is bubbling with stories about internal Romney campaign squabbles, with some even questioning whether Romney himself screwed up the organization of the campaign’s internal mechanisms of authority and accountability. Stories also questioned whether the Clint Eastwood convention debacle resulted from poor planning. The trip abroad was widely criticized as insufficiently thought through. Even Republicans have asked whether Romney’s hasty reaction to the attacks on the Embassies risked undermining impressions of his leadership abilities. As Peggy Noonan writes today, he came across as “small and tinny” at “one of those moments when people look at you and imagine you as president.”

Democrats will be closely watching in coming days to see if polling shows an erosion in public impressions of his managerial skills and leadership aura. This had previously been a strength, with many voters proving willing to grant him the presumption, based on his success in business, of management and turnaround abilities; polls had steadily shown him enjoying an advantage over Obama on who is more trusted to handle the economy.

A Democrat points out the following numbers. A Fox poll finds Obama leading Romney 50-40 on who is a steady leader. An NBC/WSJ poll finds Obama leading 47-36 on who is better prepared to lead the country for the next four years. A Post poll finds Obama leading 50-42 on who is the stronger leader. And a CNN poll in early September found Obama taking a small lead on who can manage the federal government effectively, 48-45, a turnaround from August.

Obviously, the race could still shape up as a referendum on Obama’s handling of the economy and little else. And Romney has another chance to project leadership qualities and managerial competence when he’s standing alongside Obama at the upcoming debates, a moment when many voters will be seriously tuning in for the first time to decide if they can picture Romney as president. But if there are more botched political responses to major campaign events, or more stories about internal campaign turbulence, Democrats will be watching to see if it creates what you might call a “leadership gap” between the two presidential contenders.