Control of the Senate appears likely to flip from the Democratic Party to the Republican Party this fall, as one of the nation’s most endangered Democrats, Senator Jon Tester of Montana, trails his Republican challenger in his bid for re-election, according to a new poll from The New York Times and Siena College.

Mr. Tester, who first won election to the Senate in 2006, is winning over moderate and independent voters and running far ahead of the Democrat at the top of the ticket, Vice President Kamala Harris. But as of now, that does not appear to be enough to survive in Montana, a conservative state where former President Donald J. Trump is ahead by 17 percentage points and where control of the Senate hangs in the balance.

Tim Sheehy, a wealthy Republican businessman and a former Navy SEAL who has never held public office, leads Mr. Tester 52 percent to 44 percent, the poll shows. Mr. Sheehy’s lead is a seven-point advantage without rounding.

Democrats currently hold a 51-seat Senate majority. But with Republicans already set to pick up a seat after the retirement of Senator Joe Manchin III, an independent from West Virginia who caucuses with Democrats, the party cannot afford to lose additional seats.

In fact, the party’s only hope is to secure a 50-50 split and to have Ms. Harris win the White House, allowing her running mate, Tim Walz, to provide the crucial tiebreaking vote as vice president.

At least seven other Democratic-held Senate seats are competitive this fall, including in the presidential battlegrounds of Arizona, Michigan, Pennsylvania, Nevada and Wisconsin. In late September, a series of Times/Siena surveys in four of those races, as well as in Ohio, found Democrats ahead, though narrowly in some cases.

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