Seattle ? Chewing over Internet policy with Silicon Valley techies at breakfast. A lunchtime speech to earnest environmentalists in San Francisco. Cocktail-hour mulling the new economy and foreign affairs with lawyers and businesspeople at a downtown Seattle office glistening with blond wood, modern art and funky African sculpture.

That might have been the prototypical blue-state itinerary for Al Gore in 2000. But one day last week, it was the schedule of Sen. Joseph I. Lieberman, D-Conn., Gore’s affable running mate. And therein may lie the promise and peril for Lieberman as he joins the flock of Democrats now exploring, with increasing tempo, possible bids for the party’s 2004 presidential nomination.

Lieberman is potentially attractive to many of the same elements in the party who like Gore. Indeed, some who backed Gore in 2000, particularly those tied to the centrist Democratic Leadership Council, would quietly prefer that Lieberman take the spotlight next time. Says one DLC insider: “I don’t think there is much enthusiasm in the DLC for Gore. … Most of our troops think it was a slam dunk last time for Gore and he blew it, or at least turned a five-point win into a tie. There’s a little buzz about (North Carolina Sen.) John Edwards among DLC people. But if we had any real favorite, it would be Joe.”

The problem for Lieberman fans is that for now it’s a moot question how he might compare with Gore in 2004. Publicly and privately, Lieberman insists that out of loyalty, he won’t run if Gore does. “That came from my gut and I’m going to stick with it,” Lieberman says.

Yet it’s clear that as Lieberman explores the race, he’ll face steady encouragement to reconsider. On his West Coast tour, he was enthusiastically received at each stop. At the breakfast in Silicon Valley, several executives emerged giving him high marks on high-tech policy. He stirred his small audience at the Seattle cocktail hour with a denunciation of President Bush’s tax cut. And later that evening, he was greeted with a steady stream of young well-wishers pledging support at a stylish Seattle restaurant where diners seemed more likely to recognize the surviving members of Nirvana than a visiting politician.

It has all left Lieberman in an oddly contingent position as rivals such as Edwards and Massachusetts Sen. John F. Kerry aggressively sow early seeds. On the one hand, Lieberman has benefited enormously from the exposure he earned as Gore’s running mate; a recent Los Angeles Times poll found Lieberman clustered with Washington’s two most prominent Democrats Senate Majority Leader Tom Daschle of South Dakota and House Minority Leader Richard A. Gephardt of Missouri as the second tier (distantly) behind Gore in an early measure of rank-and-file sentiment for the 2004 nominee. Kerry and Edwards barely registered.

On the other hand, the prospect that Lieberman might eventually defer to Gore could make it tougher for the Connecticut senator to line up firm commitments from activists, fund-raisers and other elected officials. “Lieberman is lagging behind in the infrastructure assets game,” insists a top operative for one potential rival. One Democratic fund-raiser at the Silicon Valley stop said that while Lieberman “was incredibly well received out here,” few were yet even thinking about him as a potential nominee. “The one who is just out here all the time,” the fund-raiser added, “is Kerry.”

Still, as the tortoise in this early maneuvering, Lieberman is demonstrating some potential strengths. He’s raised money steadily ($1.2 million last year) for a political action committee he formed to support other Democrats in 2002, traveled widely (he’s appeared in some three dozen cities since the 2000 election, both raising money and appearing for other candidates) and kept himself visible in Washington (he played an important role in brokering the agreement Congress reached with Bush on education reform).

When Lieberman departs from the Clinton legacy, he usually edges to the right. Even compared to other “New Democrats,” Lieberman has been more critical of Hollywood and the music industry and more hawkish on foreign policy (he’s been the leading Democrat urging Bush to remove Saddam Hussein in Iraq). By contrast, Gore’s departures have typically tilted him left of Clinton (on issues such as licensing gun owners).

Which means that even if Gore doesn’t run, a Lieberman candidacy would test the boundaries of acceptable heresy from conventional liberalism in a Democratic primary. His boosters believe Lieberman’s muscular foreign policy and strong appeal to cultural conservatives on values issues fit the profile Democrats will need in a general election against Bush, who’s likely to be strong on both fronts. But in the primaries, those views won’t be easy to sell to dovish schoolteachers in Iowa or secular young professionals in New Hampshire.

Before Lieberman can worry about any of those voters, he’ll need to resolve his minuet with Gore. For all their personal affinity, the two men already may be subtly jostling. Some Democratic foreign policy experts thought Gore’s recent call for action against Iraq may have partly reflected a determination not to allow Lieberman to his right. And Lieberman’s pitch to Silicon Valley and environmentalists last week caused some of the former vice president’s California supporters to wonder if the Connecticut senator was firing a shot across Gore’s bow. Lieberman says he has no inside information on Gore’s intentions. But as Lieberman bustles exuberantly from event to event, a happy warrior if ever there was one, it doesn’t take any inside information to know exactly what he hopes Gore will do.