"NPP voters often show you which way the wind is blowing on something like this where it’s a partisan issue," DiCamillo added.
Among voters not reminded of Feinstein's age, 56 percent say they'd be inclined to vote for her, while 44 percent would not be. But among those reminded that she'd be 84 next year, it's split right down the middle, with 50 percent saying they'd be inclined to vote for her and 50 percent saying they would not.
But here's a twist: When voters are asked to choose from a list of candidates they'd support if Feinstein does not seek re-election, Jerry Brown, who will be 80 next year, receives support from the highest percentage of voters (23 percent), followed by Fresno's former mayor, Ashley Swearengin, a Republican (22 percent).
The rest, including Los Angeles Mayor Eric Garcetti (8 percent), congresswoman Jackie Speier (7 percent), congressman Adam Schiff (5 percent) and Attorney General Xavier Becerra (4 percent), are all in single digits. Twenty percent of those polled are undecided.
What does pollster DiCamillo make of senior statesman Brown leading among voters who seem to think Feinstein might be too old?
"It's not as if they're necessarily just looking for someone younger," DiCamillo said, "but Jerry Brown would represent someone new and different in Washington."
That said, Feinstein, whose seniority gives her tremendous power in the Senate, would not be easy to beat.
"Certainly, incumbency has its advantages, so for candidates to be considering running against her, that would be formidable," DiCamillo notes.
Feinstein is taking steps to fend off a potential challenge from her left, such as opposing the nomination of Supreme Court nominee Neil Gorsuch and speaking out strongly against the Trump administration.
And the reality of taking on a popular incumbent is complicated, says Thad Kousser, chair of the UC San Diego political science department. "People might want a new face in California politics but it's still Sen. Feinstein's seat to give up," he says."If she decides she has the energy and passion to stay in the office, she'd be very hard to beat."
The poll also found California's junior senator, Kamala Harris, with 53 percent approval among registered voters. Twenty-seven percent disapproved of her performance as senator, while 20 percent had no opinion.
The Berkeley IGS poll is based on 1,000 California registered voters conducted by the Institute of Governmental Studies at UC Berkeley. The poll was administered online by YouGov March 13-20, 2017. It has a margin of error of +/- 3.6 percent.