Washington ? John Kerry can congratulate himself on a successful vice presidential choice. But if he is realistic, he will recognize that the heavy work of winning this election still lies ahead of him.

The most recent Washington Post poll, taken July 8-11, showed the Democratic ticket of Kerry and John Edwards tied with the Republican duo of George Bush and Dick Cheney at 46 percent. Ralph Nader had 4 percent.

In a series of polls going back to March, when he clinched the presidential nomination, Kerry has led by no more than 4 points, Bush by no more than 5. That is what you call a toss-up.

In the time since Kerry picked erstwhile presidential rival Edwards for his running mate, I have seen six other polls. Four put Kerry out front; two had Bush leading. Averaging their results, Kerry is at 47 percent; Bush, at 45; Nader at 4. Again, a statistical tie.

That is not a bad position for a challenger on the eve of his convention. But almost every politician I asked about these numbers agreed that the Massachusetts senator has heavy lifting ahead of him.

Why? First, because he has probably received most of the benefit he will ever get from placing Edwards on his ticket. The choice of the first-term senator from North Carolina clearly went down well. Kerry knew going in that Edwards was the favorite of rank-and-file Democrats. The following Edwards won for himself in the primaries last winter was second only to Kerry’s.

The polls make it clear that Edwards also has done well with the broader range of voters. In the Post poll, twice as many people said the selection of Edwards made them think more favorably of Kerry as said it diminished their respect for him. Time magazine reported that by a margin of 47 percent to 38 percent, its sample said Edwards would make a better president than Cheney. Newsweek reported that those it polled said that if they could vote separately for vice president, Edwards would win 52 percent to 41 percent.

That’s a pretty strong endorsement of Kerry’s choice — but it doesn’t seem to have bolstered Kerry’s performance against Bush, which is really what counts. The TV, newspaper and magazine spreads on Edwards last week were more extensive than the attention he is likely to get at any point later in the campaign. As a booster rocket for the ticket, his fuel is mostly spent.

Meanwhile, the Kerry-Bush stalemate continues, even while the president continues to be buffeted by events. A unanimous bipartisan report from the Senate Intelligence Committee documented the failings of the CIA in assessing the threat from Iraq, blowing a huge hole in Bush’s claim that war was required to eliminate weapons of mass destruction and sever an alliance between Saddam Hussein and al-Qaida.

The handover of authority to an Iraqi interim government has not brought the hoped-for cessation of violence or a break in the casualty reports for Americans and Iraqis. The Philippines has led an exodus of small countries from the “coalition of the willing” backing U.S. forces in Iraq.

And at home, the administration has issued dire new warnings of possible terrorist attacks between now and Election Day, while a wobble in the economy — a sudden sharp drop in consumer spending — raised anxiety about the recovery.

With all this happening, one might have expected something of a Kerry surge. Democrats I interviewed are both puzzled and dismayed that it hasn’t happened. Their explanation — supported by the polls — is that Kerry has not yet sold himself to swing voters as an alternative to Bush. Ed Rendell, the governor of Pennsylvania and a former chairman of the Democratic National Committee, told Judy Woodruff of CNN, “To be honest, even though we had a pretty active primary season … most American people don’t even believe that they’re familiar with John Kerry yet.”

Mark Mellman, Kerry’s pollster, told my Washington Post colleague John Harris, “There’s a lot of people who don’t know enough about John Kerry to make a judgment about him and his values.”

A Democratic senator put it more bluntly: “They haven’t warmed up to him, and I don’t know if they ever will.”

Next week in Boston, at the Democratic National Convention, Kerry will have his best — and perhaps his last — chance to put his own stamp on this race. He cannot afford to miss it.

David Broder is a columnist for Washington Post Writers Group.