She's the oldest U.S. senator, and she's staggeringly popular with her constituents — at least until you remind them that she's the oldest U.S. senator.

Then voter enthusiasm dips for 83-year-old Dianne Feinstein, according to a new poll, and the dip may be enough to raise some questions about a Feinstein run for a sixth term in 2018.

The poll, conducted by the University of California, Berkeley Institute of Governmental Studies, asked 1,000 registered California voters if they thought Feinstein running for re-election would be "a good thing for California." About half of respondents — 48 percent — said Feinstein on the ballot in 2018 would be good for the state.

But among voters who were reminded that Feinstein will turn 84 next year, that dropped to 38 percent, with 62 percent saying another Feinstein campaign would be bad for the state.

"Even though I myself am up there in years, there comes a time — particularly in political circles — to allow younger people to come up," said John Hansen, 79, of Castro Valley, who calls himself a big admirer of Feinstein but thought it was time for her to make room for someone younger.

Ironically, Californians' top candidate to succeed Feinstein if she chooses not to run for re-election is Jerry Brown, who's turning 80 next year, the poll found.

Feinstein, who has been in office since 1992, is the oldest currently serving U.S. senator, though she has a way to go to match Strom Thurmond, the South Carolina senator who retired in 2003 at 100. She's signaled that she's running for re-election — holding a fundraiser for her campaign last month in Los Angeles — although she hasn't made a formal announcement one way or another. She had a pacemaker installed in January in what her office said was a "routine, voluntary" procedure.

Despite her years, she remains a formidable politician: Even though 62 percent of voters reminded of her age said her running again would be bad for California, 50 percent of those reminded said they would vote for her if she ran. And overall, 59 percent of respondents say they approve of the job she's doing in Washington, D.C., where she's the ranking Democratic member of the Senate Judiciary Committee.

"There may be people out there who think it's time for a change with some new blood for the Senate," said Mark DiCamillo, the director of the poll. "But when you ask a direct question, even some of the people who have some reservations are inclined to support her."

If Feinstein, a former San Francisco mayor, decides not to run, 2018 would be a banner year for California politics: the first election in the state since 1982 with simultaneous open seat races for the governorship and U.S. Senate. The governor's race is already crowded with a who's-who of state politicians, and a similarly broad field of candidates could be expected for an open-seat Senate race.

Brown would be the top candidate to succeed Feinstein if she bowed out, the poll found. "He's probably the most popular politician in the state," DiCamillo said. Brown racked up 23 percent in a list of potential candidates, with former Fresno Mayor Ashley Swearengin, a Republican, in second at 22 percent and Los Angeles Mayor Eric Garcetti in third with 8 percent.

There's no real sign that Brown, who ran for U.S. Senate in 1982 and lost to Republican Pete Wilson, is considering another run. However, former San Francisco Mayor Willie Brown floated the idea in a December column in the San Francisco Chronicle. At an event last week, Gov. Brown joked that "I'll be moving to the ranch in two years" when he is termed out as governor — but when asked about another presidential run, he said, "Don't rule it out!"

So when will Feinstein make up her mind? The Los Angeles Times asked her on April 1, 2016, whether she'd run for re-election. "Ask me that in about a year," Feinstein said. "I'll give you the answer then."

One year and two days later, no answer yet: Feinstein's office didn't respond to a request for comment. (Brown's office also didn't respond.)

Her announcement, one way or another, will mark the unofficial kickoff of the Senate campaign. "It's a very personal decision on her part, whether she has the fire in her belly to run again," DiCamillo said. "It's very wide open if she chooses not to run, and if she does, she'll be very formidable."

Several voters in the San Francisco Bay Area said they think Feinstein should stay in the Senate.

"She's like an icon," said Jewel Taylor, 65, who lives in San Jose. "She's old school, she's been around this planet for a little while, and she knows the ins and outs. I think we need people like that in our society right now."

Others are ready to see her go. "She's extremely old, and I wonder if she can make it through another election," said Paul Loverde, 53, who lives in Berkeley. "I think she's out of touch. She's been there too much; she doesn't know anything except Washington."

Hansen said he is a longtime follower of Feinstein's political career. But he argued that "there are a lot of good people in the Democratic Party in California who are being held in place until she decides to retire." Hansen's suggestion for Senate: his congressman, Eric Swalwell, who got 2 percent in the poll of potential candidates.