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Like an Oscar winner with a stain on his tuxedo or a beauty queen with an untimely zit, Barack Obama and John McCain are each confronting one large blemish as they prep for their big day.

Each presumptive presidential nominee will arrive at his national convention--Obama in Denver next week, McCain in Minneapolis-St. Paul the week after--facing one overriding obstacle. Conventional wisdom holds that the candidate who best solves his own problem will win in November. But that may be too simplistic. For Obama and McCain, magnifying the other guy's problem may be at least as important as resolving their own.

By now, each nominee's principal weakness is familiar--and largely a mirror image of the other's. Obama faces doubts about whether he possesses the experience and qualifications to serve as president, particularly as commander-in-chief. McCain faces doubts about whether he possesses the energy and vision to chart a new course for a deeply discontented nation--or will follow too closely in the ruts left by the departing George W. Bush.

For many undecided or loosely committed voters, Obama appears too green and McCain too gray; Obama too great a leap into the unknown and McCain too much an extension of the status quo. As one undecided man in the pivotal Denver suburbs told me last month, "I think McCain is a little over the hill, which makes me nervous. I think Obama doesn't have a lot of experience, which makes me nervous."

Polls underscore the breadth of such sentiments. In an August survey by the independent Pew Research Center for the People and the Press, McCain led Obama by 2-to-1 when voters were asked which candidate was personally qualified to be president. Among those the pollsters identified as swing voters, McCain held a more than 4-to-1 lead. Swing voters also preferred McCain over Obama by 2-to-1 when asked which candidate would use good judgment in a crisis. On the other hand, when asked which candidate offers new ideas, swing voters preferred Obama over McCain by almost 8-to-1. Even among McCain supporters, Obama led by 20 percentage points as the candidate of new ideas. Ouch.

Both candidates have already devoted enormous energy to combating those negative perceptions, and each will have more opportunities to do so until November 4. But some strategists in both parties question whether either will make much progress. David Keene, chairman of the American Conservative Union, expresses a view common among operatives outside of both campaigns when he says, "I don't know how either one of them overcomes their problem."

Recent evidence supports that skepticism. Obama's trip abroad last month offered him as visible an opportunity as can be imagined to burnish his national security credentials. Yet a post-trip CBS poll showed that just one-fifth of voters thought it was "very likely" Obama would be an effective commander-in-chief, slightly less than before he left. Likewise, McCain has released a stack of policy proposals this year without much denting the sense that he offers more continuity than change. It's not clear what else McCain can do to dispel that notion, short of renouncing Bush on Iraq and taxes, or somehow shedding 20 years.

If neither candidate can entirely fix his own problem, the more relevant question may be which can more effectively compound his rival's. "As long as the other guy doesn't solve his problem," said Democratic pollster Mark Mellman, "you can win without solving yours." McCain's camp already seems to be operating on that conclusion: It has palpably shifted its focus from bolstering McCain to questioning Obama's qualifications through pointed (even derisive) ads portraying the Democrat as a vapid celebrity.

Obama seems more ambivalent about his focus. Before his August vacation, Obama sharpened his attempt to link McCain to Bush and to business as usual in Washington. But, mostly, Obama has concentrated on reassuring voters about his qualifications, to the point where one top Democratic strategist frets, "They are so into reassurance they are losing all passion." That was the complaint many Democrats leveled at John Kerry's campaign after the 2004 convention focused much more on overcoming Kerry's weaknesses than highlighting Bush's. When Obama accepts his historic nomination at Denver's Invesco Field on Thursday, many senior Democrats will be anxiously watching to see whether he plays mostly defense--or offense.