WASHINGTON – Just one week after voting against the confirmation of Justice Alito to the Supreme Court, New Jersey’s new Democratic senator faces another thorny political decision: Whether to support a wiretapping program that President Bush has credited with helping to avert another terrorist attack on American soil.

Senator Menendez, a former congressman who was appointed senator when his predecessor, Jon Corzine, was elected governor of New Jersey, was already taking heat over his support for blocking Justice Alito, a New Jersey native, to the high court when Republicans decided to make Democratic opposition to the wiretapping program an issue in the November elections.

A handful of Republicans, including the chairman of the Senate Judiciary Committee, Senator Specter, of Pennsylvania, have raised questions about the legality of the program, with Mr. Specter saying on NBC’s “Meet the Press” that the Bush administration’s legal reasoning has been “strained and unrealistic.” Mr. Specter will open a hearing on the National Security Agency program today.

But Mr. Bush and the majority leader of the Senate, Senator Frist, of Tennessee, have defended the NSA program, describing it as an essential tool in the war on terror. Polls show that a majority of Americans support the NSA program despite Mr. Bush’s low approval ratings. A mention of it drew loud applause from Republicans and silence from Democrats during last week’s State of the Union address.

“If there are people inside our country who are talking with Al Qaeda, we want to know about it,” Mr. Bush said. “Because we will not sit back and wait to be hit again.”

Though a popular target of liberal Democrats, the wiretapping program is nettlesome for senators like Mr. Menendez who face close races next year. A recent Rasmussen Reports poll showed that a state senator and son of a popular former Republican governor of New Jersey, Thomas Kean, leads Mr. Menendez 42% to 35%. A Rasmussen poll from December showed Mr. Kean trailing Mr. Menendez by four percentage points.

“I think you’ll see us distributing information on the security issue to reporters in New Jersey and to our supporters in the state encouraging Democratic candidates for Senate to say what they think about domestic surveillance,” a spokesman for the National Republican Senatorial Committee, Dan Ronayne, said. “This is an important issue, and we want to see where the candidates stand.”

So far, Mr. Menendez has tried not to make an issue of the program, raising questions about its potential illegality but skirting questions about its usefulness. A spokesman for Mr. Menendez, Matthew Miller, told The New York Sun yesterday that Mr. Menendez would wait for the results of the hearing before making a final judgment on it. In a sign that Democrats aim to take cover behind Republican critics of the program, Mr. Miller pointed out that both parties have raised questions about the program.

“This is more important than politics,” Mr. Miller said. “The question is whether the president acted within the law, and the answer to that question is more important than politics. I think we need to see what the investigation yields and what the hearings yield.”

Political analysts said Republicans would be smart to play up security issues in an election year that is shaping up to favor Democrats. Some have pre dicted the majority party could lose its edge in the House of Representatives and the Senate in the wake of cascading scandals. But others say that Republicans could limit the damage and even make perennially Democratic states like New Jersey competitive by focusing on security.

“Republicans are correct in their evaluation that most Americans, when push comes to shove, will support the president on security because of fear of terrorism,” the director of the University of Virginia’s Center for Politics, Larry Sabato, said. “And frankly, the surveys show that. This is a civil liberties issue that plays very well with the elites and, as usual, the elites are outnumbered. You can’t find anyone at a university who is supportive of wiretapping, but they don’t come close to being a majority.”

Republicans are focusing on New Jersey, a strongly Democratic state that hasn’t had a Republican in the Senate since 1979, in the hopes of forcing the opposition party to spend money in a state about which it doesn’t ordinarily have to worry. Mr. Sabato predicted that Mr. Menendez will win the race, but that Republicans could benefit in other states by making national Democrats, who have far less money to spend than Republicans, expend resources on his campaign.

Still, other analysts said Republicans could suffer from playing up the security threat. They said a close association between Republican candidates and Mr. Bush could mean trouble.

“The Democratic Party is in bad shape and messageless,” the president of Zogby International, John Zogby, said. “And terrorism could work for the Republicans this year overall. It’s just that in New Jersey aligning yourself with President Bush is not necessarily a plus.”