Half of likely California voters doesn't want to see Sen. Dianne Feinstein Dianne Emiel FeinsteinBiden leads Trump by 12 points among Catholic voters: poll Names to watch as Trump picks Ginsburg replacement on Supreme Court McConnell says Trump nominee to replace Ginsburg will get Senate vote MORE (D) run for another term, according to a poll released Thursday.

A new Public Policy Institute of California poll finds that 46 percent of Californians don't believe the long-serving senator should run for a sixth term in 2018. That percentage increases to 50 percent when narrowed to include only "likely voters."

Just more than half of Democrats in the state, 57 percent, say Feinstein should run for reelection, but she is underwater with independent voters. More than half of independent voters, 55 percent, want Feinstein to retire at the end of her fifth term in January.

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A majority of likely voters, 54 percent, approve of the job she is doing, including 71 percent of Democrats.

California's other Democratic senator, Kamala Harris Kamala HarrisJoe Biden looks to expand election battleground into Trump country Fox's Napolitano: Supreme Court confirmation hearings will be 'World War III of political battles' Rush Limbaugh encourages Senate to skip hearings for Trump's SCOTUS nominee MORE, is less well-known than Feinstein, according to the poll, but has a higher level of support likely votes. More than half, 54 percent, of likely voters said that they approved of Harris's job performance, compared to 30 percent who disapproved and 23 percent who couldn't say.

Feinstein faces possible challenges from the party's left over her support of some of President Trump's nominees and her refusal to endorse single-payer health care.

The centrist Democrat shocked a crowd in her home state last month when he appeared to say that Trump could still have her support, explaining his potential to be a "good" president.

"The question is whether he can learn and change," Feinstein said in August. "If so, I believe he can be a good president."

She added that Trump will have to "forget himself enough and have the type of empathy and direction the country needs."

The Public Policy Institute of California surveyed 1,734 California adults via telephone from Sept. 10 to 19. The poll carries a margin of error of 3.1 percentage points.