WASHINGTON — If Democrats barely miss gaining control of the Senate next month, they may end up blaming Governor Corzine of New Jersey.

The Democrats are within striking distance of taking the Senate, pressing Republican incumbents in such states as Ohio, Pennsylvania, and Missouri. In New Jersey, though, Senator Menendez, a Democrat, appointed by Mr. Corzine to fill his own unexpired Senate term, is locked in a tight race in a state that hasn’t elected a Republican senator since 1972.

Democrats need to gain six seats to take control of the Senate, and if a New Jersey loss makes the difference, “Corzine would have to accept some of the blame,” Jennifer Duffy, who tracks Senate races for the nonpartisan Cook Political Report in Washington, said. “He was Corzine’s hand-picked choice and the first major decision he made as governor.”

For Messrs. Menendez, 52, and Corzine, the issue is whether the senator’s ties to a scandal-tinged political machine will repel voters tired of corruption allegations involving the state’s dominant Democrats.

Meanwhile, the Republican nominee, state Senator Thomas Kean Jr., has his own issues, principally whether the pull of one Republican dynastic name — his father was a two-term governor and chairman of the commission charged with investigating the September 11 terror attacks — is strong enough to counter the drag of another: President Bush.

Mr. Corzine picked Mr. Menendez, then a congressman, from among a field of Democratic lawmakers eager for the appointment on the theory that he could run the strongest statewide race. That hasn’t been borne out so far.

The latest blow came from a September 28 article in the Newark Star-Ledger reporting that Mr. Menendez’s closest political ally was taped trying to convince a contractor to hire someone as a favor to the senator.

The story spurred speculation, fanned by Republicans, that Mr. Menendez might be forced from the ballot and replaced with another candidate, as happened in 2002 when Senator Torricelli, a Democrat, also dogged by ethics charges, stepped aside in favor of a former senator, Frank Lautenberg, who won.

Mr. Menendez dismisses such chatter. “I’m not going anywhere,” he said in an interview.

Campaigning on October 1 in Hudson County, surrounded by well-wishers honoring him as the man of the year at the Hispanic Statewide Parade, Mr. Menendez said he isn’t surprised that Mr. Kean, 38, has waged a competitive battle.

“I’m not a traditional incumbent; I’ve been an incumbent for nine months,” Mr. Menendez said. “The electorate doesn’t know much about either one of us except for my opponent’s surname.”

That surname remains a potent one, synonymous with a patrician tradition of public service. Mr. Kean’s father, who as governor starred in a long-running series of television commercials boosting tourism — “New Jersey and you, perfect together” — remains one of the state’s most visible and popular political figures. Kean University can be found in Union.

The younger Mr. Kean “benefits from the brand,” Mr. Duffy said.

Still, he started the race as an underdog. He began his political career only five years ago, when he was appointed to a seat in the state Assembly, and has never before run for statewide office. Moreover, he’s running in a state where registered Democrats outnumber Republicans and that hasn’t voted for a Republican for president since 1988.