United Democrats began assembling here Saturday for a national convention designed to introduce Sen. John F. Kerry to the country, convince voters that he can lead a war against terrorism and show that he offers an appealing alternative to President Bush and the Republicans.

With an eye on undecided and swing voters, Kerry and the Democrats begin their convention week exuding confidence, buoyed by surveys showing that the public has more faith on many issues in the Democratic Party than in the Republican Party and that voters remain critical of Bush's handling of the two dominant issues in the campaign, Iraq and the economy.

But the Democrats' self-assurance exists despite the reality that Kerry has struggled to turn broad dissatisfaction with Bush's presidency into stronger support for his own candidacy. Most pre-convention polls continued to show the presidential race still within the margin of error, and Democrats see the convention as a critical opportunity for Kerry to change the shape of the contest.

"He's not closed the sale," independent pollster Tim Hibbits said of Kerry in an interview. "Basically his strongest strength is he's not George Bush."

Officials here were rushing to complete preparations for what may be the most unified Democratic convention in recent memory, as thousands of delegates, activists and journalists began arriving to find a city heavily secured against threats of terrorism. Meanwhile, labor negotiations continued between the city and the firefighters union in a final attempt to head off potentially disruptive picketing at some convention-related events.

After 18 months in which Democratic candidates and party leaders have pounded the president, Democratic officials promised to put on a positive show this week, at least from the podium inside Boston's FleetCenter. "This is going to be a positive convention," New Mexico Gov. Bill Richardson, the convention chairman, told reporters Saturday at a breakfast hosted by the Christian Science Monitor. "This is not going to be a bash-Bush convention."

Over four nights beginning on Monday, Democrats from former president Bill Clinton to Massachusetts Sen. Edward M. Kennedy to Kerry's running mate Sen. John Edwards will highlight Kerry's biography as a combat veteran with two decades of Senate experience, while rebutting Republican criticisms that he is too liberal and lacks convictions on critical issues.

"We've got to make the affirmative case, not the negative case," said Arizona Gov. Janet Napolitano, who is on the convention program. "There is no doubt that the Democratic base is motivated."

Republicans will be here in force all week to challenge what they dub the "extreme makeover" of Kerry at the convention from a politician with one of the most liberal voting records in the Senate to one who presents himself as being far closer to the center of the political spectrum. "This is someone who has a 19-year record on key issues of taking positions way out of the mainstream," said Bush-Cheney campaign manager Ken Mehlman.

The Democrats' determination to project a positive tone at the convention reflects their view of how the race may be won in November. With rank-and-file Democrats thoroughly energized around the goal of denying Bush and Vice President Cheney another term in office, Kerry campaign and party officials hope to use their convention to broaden the candidate's appeal to undecided and swing voters who may hold the key to victory if the race stays as close as it has been.

"People are living the critique of the Bush administration," said Kerry campaign manager Mary Beth Cahill. "I think that now it's about the future and it's about where will John Kerry lead the country. I think people will certainly talk about Bush, but this is more about Kerry and Edwards."

Kerry alluded to those voters in an interview with ABC's Peter Jennings last week when he said he would be thinking as much about his television audience as the delegates inside the hall in Boston when he delivers his acceptance speech on Thursday night. Asked whether he would turn up the volume from his normal stump speech style, he said, "I think you have to remember that you're talking to a television set as much as you're talking to hall."

The Democratic gathering here brings to an end an intensive pre-convention campaign period that has seen both sides raise and spend record amounts of money, much of it spent on television advertising in about a dozen-and-a-half battleground states. But for all the activity, the margin between Kerry and Bush has moved little.

Nor did Kerry's selection of Edwards as his vice presidential running mate significantly shift the race in the Democrats' direction. The two sides are now engaged in a game of expectations over how much of a post-convention bounce in the polls Kerry should expect. Bush-Cheney chief strategist Matthew Dowd argues that, based on history, Kerry should see a 15-point swing, while Kerry officials say that with so few genuinely undecided voters, the bounce will be far more modest.

Those arguments aside, the Democrats said they start their convention ahead of where some past challengers have been. "When you look at past conventions, people are trying to do what Kerry has already done, consolidate their party and try to bring unity to it," Cahill said. "We've accomplished that already."

A new poll by the Pew Research Center found the Democrats' image is significantly better than it was on the eve of the 2002 midterm congressional and gubernatorial elections, when the Republicans made historic gains. On both the economy and terrorism, the Democrats have gained ground and are now seen by the public as better equipped to deal with the economy and about even with Bush and the Republicans on terrorism, where Bush once held a big advantage.

But GOP pollster David Winston said that the electorate is not trying to assign blame but trying to determine what each candidate plans to do about the country's problems. "That's a net positive because we're the party in power," he said.

Democrats argue that, while Kerry still must answer voters' questions about him starting this week, the election shapes up far better for him than for Bush. Democratic pollster Stan Greenberg said about 55 percent of the public wants a change in direction. "Kerry runs with a majority in front of him that wants change," Greenberg said. "He's got to demonstrate that he's the person who can lead, but the majority for change seems pretty well established."

Simon Rosenberg of the centrist New Democratic Network said Kerry is in a stronger position than Bush because the president has to make up lost ground among the voters. "Bush has to go get back what he had, which is very hard," he said. "I would rather be us than them right now."

But key Bush advisers and their Republican allies said they see a possible turn in the president's direction. "External events have dominated but if that's the case then it makes me feel even better," said a top Bush political adviser. "The president's approval rating is firming up, the numbers on the economy are firming up and Democrats, instead of getting a big bounce [from Edwards's selection] got a brief bounce that quickly washed away. So the fundamentals are firming up for Bush."

Several GOP pollsters said with external events so dominant in this campaign, Bush may look forward to better news in the months ahead that could shift the electorate in his direction. "This President Bush has time for the economy to help him far more than his father did in 1992," said Whit Ayres, an Atlanta-based Republican pollster. "The economy started growing six months earlier than it did in 1992."

Republicans see Iraq as a wild card that yet could work to Bush's benefit if U.S. casualties diminish and the new interim government is seen as taking hold successfully. But several Democratic governors interviewed in the past week said there is little evidence that the transfer of power there has shifted attitudes among their constituents in the president's favor.

The Democrats plan to make Kerry the singular focus of their convention this week in the hope that he can fill out a profile that remains only partially completed in the minds of many voters.

The Bush campaign's Mehlman said Kerry so far has failed to do what Bill Clinton and Jimmy Carter, the two successful Democratic candidates of recent decades, had done by the time of their conventions. "The only Democrats who have succeeded have defined themselves as being different kind of Democrats," he said. "It's hard to argue that John Kerry has done that" since wrapping up his nomination.

William Mayer, a political science professor at Northeastern University here, said Kerry's Massachusetts roots and campaign style remain obstacles as he attempts to connect more directly with voters. "Whatever else you want to say about Clinton, he had a much clearer positive message than Kerry does," he said.

Two Democratic governors, Bob Wise of West Virginia and Mark R. Warner of Virginia, said they saw a far more positive candidate in recent campaign appearances in their states. "In Charleston, I saw this guy begin to connect with the crowd," Wise said.

But Oregon Gov. Ted Kulongoski (D) said he believes more needs to be done. "I just don't think Kerry has come across in identifying himself in any particular way," he said. "I think you have to do something, be much more specific with the voters."

Kerry hopes to use the convention to do that but in an environment that no recent challenger has confronted, one in which terrorism has reshaped the presidency and to some extent the voters' checklist of what they want in a commander in chief.

Democratic and Republican strategists see swing voters in particular as torn between a desire for a new direction and a reluctance to change presidents in such an unsettled time. As GOP pollster Ayres put it, "Any reelection campaign is a referendum on the incumbent, but to say that implies that the challenger doesn't matter, and I don't believe that is the case, particularly in a time of war. The challenger matters a lot when the country is under attack."

The next week will begin to answer the question of whether Kerry can begin to cross that threshold successfully.

From left, Chris Burns, Scott Allen, Rod Sullivan and Jack Varney install bunting for the convention in Boston.