A man walked up to me in a store on Nantucket, where Sen. John Kerry (D-Mass.) vacations, and said he’d known Kerry for 25 years. Their kids went to school together, he said.

“So, do you like him?” I asked.

“No,” he said. “Can’t stand him. He’s arrogant. He’s cold. And he’s mean.”

“So you’re going to vote for Bush,” I said.

[IMGCAP(1)] “I don’t think I can,” he said. “I’ve voted Republican all my life, but I can’t support Bush. We had no business invading Iraq and he’s made a terrible mess of it.”

“So who are you going to vote for?” I asked.

“I just don’t know,” he said.

On the basis of random talks with dozens of voters in various places around the country, on the basis of unscientific polls I’ve taken and on the basis of public polls I’ve studied, I’d say this man isn’t alone. In fact, he and conflicted voters like him just may decide the outcome of the November election.

I ask people: Do you know anybody who voted for Al Gore in 2000 and is planning to vote for Bush this time? And, what about people who voted for Bush, but are switching to Kerry?

Anecdotally, there aren’t very many in the first category but a fair number in the second — people troubled by Iraq, by Bush’s uncompassionate conservatism or by his lack of fiscal restraint.

But public opinion polls don’t back up this assertion. The polls show that there are just as many — or, rather, just as few — Republicans leaning toward Kerry as there are Democrats planning to vote for Bush.

In a recent Web posting, GOP pollster Bill McInturff sought to puncture the myth of Republican dissension over Bush.

“There’s a sort of wave developing from people wanting to report about Republican restiveness about the Iraq war or the deficit and declining support for Bush. Huh?” In fact, he says, “President Bush enjoys unbelievably strong support among Republicans … including among Independents who say they lean Republican.”

In polling he did for National Public Radio in May with Democrat Stan Greenberg, McInturff found that only 6 percent of Republicans say they plan to vote for Kerry and 7 percent of Democrats say they’ll vote for Bush.

“Kerry Republicans?” he says. “You’ve got to be kidding.” The numbers indicate he should say the same about “Bush Democrats.”

Both presidential campaigns are doing “outreach” to the other camp, however. The Bush campaign claims to have 3,000 Democrats signed up and has announced a steering committee of 98 led by retiring Sen. Zell Miller (D-Ga.) and including former Attorney Gen. Griffin Bell, Miami Beach Mayor David Dermer and former Democratic National Committee Executive Director Brian Lunde.

A Republicans for Kerry committee is supposed to be announced at or after the Democratic convention, but Kerry has already picked up an endorsement from former Chrysler CEO Lee Iacocca, a 2000 Bush supporter.

Although Bush’s approval scores on the economy have risen, almost all recent polls have indicated a continued decline in his overall approval. Yet he’s still in a dead heat with Kerry.

The two campaigns’ interpretations of these realities couldn’t be more different. Kerry aides say that when incumbent presidents are running for re-election, the contest is basically a referendum on his performance. By this measure, they say, Bush is in deep trouble.

In four new polls out last week — the bipartisan Battleground survey, NBC/Wall Street Journal, CBS/New York Times and Fox News — Bush’s average approval rating was just 46.8 percent.

According to McInturff, that number puts Bush somewhere in between past presidents who’ve won re-election and those who’ve lost.

The average June approval rating of winning Presidents Richard Nixon, Ronald Reagan and Bill Clinton was 55.3 percent. The average for losers Gerald Ford, Jimmy Carter and Bush’s father was 38 percent.

In the Bush camp, campaign manager Ken Mehlman sees the race as “a referendum, yes, but also a choice between two candidates.” This accounts for the amount of money the Bush campaign has spent “defining” Kerry negatively.

And polls indicate that Bush’s ads are having an effect. In the Battleground survey, 56 percent of voters said that Bush is a “strong leader,” compared with 39 percent for Kerry. In the CBS poll, 58 percent said that Bush “says what he believes,” while 55 percent say that Kerry “says what people want to hear.”

Both campaigns agree that voter intensity is a key to turnout and victory — and each claims intensity is with its candidate.

Polls indicate that Bush’s intensity is based on “love,” while Kerry’s intensity is based on “hatred” — for Bush.

In the latest ABC poll, 83 percent of Bush supporters say they are voting primarily because they favor Bush, and 16 percent say they are motivated by opposition to Kerry.

The poll showed that only 44 percent of Kerry voters are strongly for him, while 55 percent say they’re primarily voting to defeat Bush.

Of course, the Kerry camp will take them regardless of their motivation. “People can be primarily voting anti-Bush and still be wildly enthusiastic about getting to the polls for Kerry,” a top Kerry strategist told me.

The NBC poll showed that 90 percent of self-defined “strong” Kerry voters and 75 percent of “weak” Kerry voters plan to “definitely” go to the polls, compared to 87 percent of “strong” Bush voters and 52 percent of “weak” Bush voters.

Kerry does seem to have this advantage: According to the Battleground survey, 92 percent of Republicans support Bush and 90 percent of Democrats support Kerry, but Kerry leads among Independents by 48 percent to 40 percent. And in the 18 most highly contested states, Kerry leads, 50 percent to 46 percent.

If the election were held today, it still seems, Kerry would win. But the election is going to be held in November. My friend on Nantucket still has four months to make up his mind.