The conventional wisdom on this presidential election is wrong.

It's frequently said that John Kerry is the man in trouble. Yes, Kerry does have a gift for getting in his own way. But President Bush is the candidate with big problems.

It's also said that the country is so polarized there is no moderate vote that matters. On the contrary, there is a very big middle that has shifted back and forth between Kerry and Bush over the past several months. That middle will decide this election.

That does not mean the election will be about who can successfully mouth centrist mush. The middle will move on the basis of events and also on judgments about which of these candidates can solve the problems these voters care about -- Iraq, health care, education costs, jobs and wages. The issue is problem solving, not positioning.

The polls over the past week portray a president in trouble. The most recent, the Pew Research Center survey released Wednesday, found that only 44 percent of Americans approved of Bush's handling of his job, down 14 points since early January. In a two-way contest, Kerry led Bush by 50 percent to 45 percent. Even when Ralph Nader was included as a choice, it was Kerry 46 percent, Bush 43 percent.

But the poll's details are what should trouble Bush. While Kerry and Bush have overwhelming support among their own partisans, Kerry led Bush among independents by seven points. Many other polls have shown independents moving away from Bush and holding pessimistic views of administration policy.

It's a long way to November, so it's useful to look at voters who say they are sure of where they stand. The Pew poll found 42 percent of registered voters saying they were certain they would vote for Kerry and 36 percent who were certain they'd vote for Bush. The hard core on each side is committed. Among conservative Republicans, 85 percent said they were certain for Bush. Among liberal Democrats, 90 percent were certain for Kerry.

But look at the middle. Among moderate and liberal Republicans, only 59 percent were certain for Bush. By contrast, 73 percent of moderate and conservative Democrats were certain for Kerry. And again, independents are a problem for Bush: 40 percent of them were sure for Kerry, only 32 percent sure for Bush.

Bush thus faces the prospect of substantial defections among moderate Republicans and has huge work to do among independents.

The central truth about presidential elections is that when an incumbent is on the ballot, the incumbent is the issue unless the challenger is utterly discredited. The Bush campaign has been spending its vast treasury not on making the case for the president but on trying to turn Kerry into an unacceptable alternative. While the Bush side has made some progress in denting Kerry's image, it has not been enough. Hostility to the president is such that, for now, voters are willing to take a chance on Kerry.

Bush's weakness in the middle reflects not only the failures in Iraq but also the president's abandonment of his "compassionate conservative" agenda in favor of a martial presidency that gambled all on the current war. He thereby made himself hostage to events far away.

David Winston, a Republican pollster, is passionate in arguing that up to 30 percent of voters are in play this year and that the incessant focus on each party's political base reflects a misunderstanding of who will decide this election. The uncertainties about Bush among independents and moderate Republicans and the big shifts between Bush and Kerry over the past six months suggest he's right.

As Winston notes, there is time between now and Election Day for the economy to grow and for the situation in Iraq to improve. And Kerry could keep playing into the stereotype the Bush campaign is creating for him. If Kerry seems to be moving toward the political center in an entirely mechanical way, the very middle to which he's appealing could come to mistrust him.

But on the current numbers, Kerry will win if he's simply good enough. Bush's task is harder: to seem a whole lot better than he does now to voters who already know him well.