The pressure is on Republican Tom Kean Jr., in Tuesday's New Jersey primary. Not to just win, as is widely expected, but to win big.

The Senate candidate and namesake son of the popular former governor figured he had a clear path to the nomination. But some conservatives decided they did not like Kean's support for abortion rights and embryonic stem-cell research.

So they put forth their own candidate, John Ginty.

Analysts say if Kean's scores anything short of a romp over Ginty in Tuesday's primary, it will signal problems in the Republican's bid to defeat Democratic Sen. Bob Menendez. New Jersey has not elected a Republican to the Senate since 1972 and Kean is seen as the party's best hope in years.

"I think it's important that the person who holds one of the most revered names in Republican politics in New Jersey comes forth with a substantial primary victory," said Clay Richards, assistant director of Quinnipiac University's Polling Institute. "He has to prove that he can do it on his own and not just on his name, and the primary will be a good test of that."

David Rebovich, director of the Rider Institute for New Jersey Politics, said if Ginty manages to get the majority of the conservative vote — 30 percent to 35 percent of the state's registered Republicans — Kean will have to figure out how to reach out to that base in November.

Menendez was appointed in January by Gov. Jon Corzine to serve out the remaining year of Corzine's Senate term. Menendez holds a slight edge in polls and a huge lead in fundraising, with more than $6 million cash on hand to Kean's $2 million.

For Kean to keep the general election competitive, Rebovich said he will need support from 90 percent or more of the state's registered Republicans, while also appealing to New Jersey's large bloc of unaffiliated voters who tend to lean Democratic.

As Kean's campaign focuses on Menendez, Ginty is coming after Kean and courting GOP voters across the state. Rebovich said Ginty campaign signs have been seen in the Trenton area, far from Ginty's home base in northern New Jersey.

"I think I have a better chance to win than a lot of people suspect, and I'm looking forward to a good performance on Tuesday," Ginty said.

Menendez's primary task is simpler but important: getting his name known to voters outside his former congressional district base in northern New Jersey. Menendez, a congressmen for 14 years, faces James D. Kelly Jr., who lives in a group home for the mentally ill.

Menendez probably will do well in New Jersey's 13th Congressional District, the area he served as a congressman. That primary race features two elections — one for the full two-year term that begins in January and the other for the last two months of the unexpired term which begins in November.

There are two Democratic candidates — Albio Sires and Joseph Vas, both mayors and state assemblymen — vying for the unexpired term in the primary. The winner will face Republican John Guarini in November; Guarini is running unopposed on Tuesday.

Sires filed to run for the unexpired term, but Vas did not. Sires' opponent for this election is James Geron. Corzine opted to hold the election for the unexpired term on primary day to save expenses.