Ron Tankiewicz had just popped a Schlitz and turned on the New York Knicks' game that night two years ago when his wife announced that the time had come.

Tankiewicz took one last look at the television - just in time to see the Knicks' great forward, Bill Bradley, swish a 15-foot jumper - and then hurried his wife to the hospital. When the baby arrived a few hours later, the proud father had already chosen a name for his new son: Bill Bradley Tankiewicz.

"Oh, it wasn't any one game," Ron Tankiewicz explained at a box here the other day. "I started reading about Bill Bradley when I was in grammar school and he was playing for Princeton. Then there was the Olympic team, and then, you know, the Knicks. And he got the Rhodes scholarship, and he wrote a good book. I always thought he was just a great person."

Opinion polls show that hundreds of thousands of Tankiewicz's fellow New Jerseyans share his admiration for head start this year in his maiden effort at politics.

Bradley, who retired from basketball last year, is seeking the Democratic nomination for this fall's race for the Senate seat held by Republican Clifford Case. The key question in the June 6 primary is whether Bradley's enormous personal popularity can be transferred from the basektball court to the ballot box.

Richard Leone, a prominent Democrat who is Bradley's chief primary opponent, seems certain that it cannot.

"I'll beat Bradley," Leone said recently. "You have to remember that I've been involved in every reform fight in this state for 10 years. What I've done matters more than what his name is."

Four other Democrats are also in the battle for the Senate nomination, on which Bradley and Leone plan to spend more than $500,000 each. But questions persist about the return on this investment.

For the winner, the likely prize is a general election contest against Case, New Jersey's most popular politician.With a voting record that perfectly suits this liberal state, and a reputation for honesty, Case is favored to win a fifth Senate term no matter which Democrat is nominated.

First, though, Case will have to turn back a primary challenge from Jeffrey Bell, a handsome intense veteran of Ronald Reagan's presidential campaign who says Case is too liberal to be a Republican standard-bearer here.

Bell likes to quote figures from Case's 1972 primary, when an unknown conservative with little money and no organization won 30 percent of the vote. Bell has spent a year organizing his campaign and raised more than $200,000 (although much of that went to pay for fundraising letters) and has received a warm reception from rank-and-file GOP voters.

In their hearts the Republicans may think Bell's right, but they seem unlikely to jettison Case and his long coattails from the top of the ticket. "As a practical political matter, we know the senator is a valuable asset," explains Leanna Brown, a GOP office-holder in Morris County.

Yet Cast has some problems.

The senator is hardly an electrifying personality - a poll late last year found that only one-third of the electorate knew who Clifford Case was. He is 74 years old, and looks it; both Bradley, 34, and Leone, 38, like to proclaim that the state needs youthful vigor in high office.

That is not the only point on which Bradley and Leone agree. On the issues, they are peas in a liberal pod. Their only real difference, and the point they talk about most on the hustings, is in the lives they led before this election.

Leone stresses his years in politics and government, as an adviser to numerous Democratic candidates and as the 1974-'76 state treasurer.

Bradley has no such experience. He can spiel off a reasonable, well-rehearsed answer on any issue, but he lacks the detailed knowledge and the governmental jargon that Leone spins out with ease. Standing with his long legs spread, gesturing with his huge hands, he cannot help but remind the audience that it's incongruous to hear a basektball player discussing foreign policy and tax reform.

Bradley tells the Democratic voters, however, that his background is a campaign asset. Whatever the electorate may think of basketball players, he says, they think even less of professional politicians. He makes it clear, too, that a star athlete is much better known than a former state treasurer, so he is the best Democrat to pit against a Republican incumbent.

Bradley's extensive name recognition has been a major boon. To counter it, Leone has hired media wizard David Garth to prepare a package of television commercials. If the Leone forces can buy enough TV time, they might overcome Bradley's advantage.

But buying time is expensive, and some Democrats say Leone's fundraising efforts have not been fruitful. Leone has reportedly found some left-wing fatcats contributing to another Democratic candidate, former state Senator Alex Menza, who can out-liberal Leone on almost every issue.

Leone, who cut his political teeth waging "reform" wars against the state's big-city political machines, has alienated some old friends by seeking machine endorsements.

The major organizations in each county have their own "line" on the primary ballot, so that machine-blessed candidates from senator down to dogcatcher are listed in the same column. This makes it easy for obedient voters to support the machine. Leone set out this spring to have his name included in the machine "line" in the biggest counties.

But Bradley came back swining. He told the county bosses that he would run a separate column, with the name "Bill Bradley" at the top and a dissident candidate for every local office, if they backed Leone. The machines backed down; in the end, Leone made the "line" in only four of the 21 counties.

That experience left a bittersweet taste with Leone, and added to an underlying hesitation that has plagued him throughout the campaign: he has no real reason to challenge the incumbent.

"It gives me pause, it really does," Leone said at a campaign stop in Princeton. "I have nothing against Cliff Case. I think he's a decent guy with a decent record.I have that hesitation about this campaign."

Bradley says he has no such feelings, but in a book two years ago, he expressed doubt whether politics could ever replace the exhilaration he knew as an athlete.

"There is a suspicion in myself," Bradley wrote, "that going into politics might be a search for the replacement of those . . . magic moments. I think of the politician standing on the podium . . . I know that when he's on the podium before that cheering crowd, he's alone; really alone."