HANOVER, N.H.-Bill Bradley, former senator from New Jersey and so far the only challenger of Vice President Al Gore '69 for the Democratic Presidential nomination, harbors no illusions.

"I know it's an uphill race," he said of his long-shot campaign at a reception here yesterday. "But it's a race I think we can win."

Bradley crisscrossed New Hampshire this weekend, trekking from local party gatherings to the Dartmouth College campus, seeking to rally support for his candidacy. Polls have shown the former professional basketball player trailing Gore among state Democrats, who will vote in the nation's crucial first primary next February.

Bradley is banking on discontent with the Clinton administration's centrist record and anxiety among New Hampshire votes over the vice president's electability in order to win support for his candidacy.

At campaign stops across the state--a state Democratic convention in Manchester, a country Democratic fundraiser in Keene, a breakfast stop at the Dunkin' Donuts in Claremont--Bradley tried to paint himself as a principled politician, willing to take on "big issues" like race relations and campaign finance reform.

Bradley has a few significant obstacles. He trails the vice-president in fundraising--he has raised $4.7 million--and many New Hampshire Democrats have already decided to support Gore.

But he has one key advantage: Democrats who aren't comfortable with Gore have nowhere else to go. And many New Hampshire Democrats question whether Gore can succeed in a general election.

"[Bradley] has to show he's more electable than Gore," said Keene Democratic town Chair Eddie Albert, "because any Democrat is better than a Republican"

Bradley has seized the opportunity, making Gore's electability a campaign issue.

"Hundred of people have come up to me and said, 'I'm an impendent,' or even, "I'm a Republican, and I'd never vote for him but I'd vote for you,'" he said in a speech to Dartmouth students yesterday.

Bradley is also running on what he calls "life experience." He grew up in Missouri, was a three-time All-American basketball player at Princeton, played for a gold-medal winning 1964 U.S. Olympic team and spent 10 years play- ing professional basketball for the New YorkKnicks before entering the Senate in 1978. Thevice president, Bradley says, has spent most ofhis life in Washington.

"I had a life before politics, I had a lifeafter the Senate," Bradley said. He claimed hisexperiences put him more in touch with theconcerns of average Americans.

Bradley offered few specific policy differencesbetween himself and the vice president. He saidyesterday he would being "exploring" theirdifferences in the fall.

He did not take a position on deploying groundtroops in the ongoing Balkan conflict, butquestioned whether President Clinton had outlinedhis goals in the Kosovo crisis clearly enough.

"When you commit forces in the post-Cold Warworld, you want to succeed," he said. "But youneed to have a clear definition of what successis."

Bradley did put forward a few ideas that hesaid would be the centerpiece of his program aspresident.