(CNN) – Gov. Deval Patrick said he's concerned that the early attention surrounding Hillary Clinton's potential 2016 presidential bid could spoil her prospects.
Asked on CNN's "State of the Union" if he thinks the former secretary of state will go "all the way" in 2016, the Massachusetts Democrat said, "I don't know."
"I guess I worry a little bit,” he continued. “She's an enormously capable candidate and leader. But I do worry about the inevitability thing, because I think it's off-putting to the average...voter."
Patrick noted that Clinton was considered the early-on favorite for the 2008 Democratic presidential primary as well but was famously bested by then-Sen. Barack Obama.
"As an enthusiastic Democrat, I just hope that the people around her pay attention to that this time around," Patrick told CNN's chief political correspondent Candy Crowley.
Patrick’s own name has been floated as a possible candidate if Clinton doesn't run for the nomination.
The Washington Post's Chris Cillizza wrote last week that the two-term governor "is a gifted speaker who would likely play well among activists on the stump. And, if he was the lone African American candidate in a Hillary-less field, Patrick would have a major leg up."
Patrick, whose term ends in 2015 and who's not seeking re-election, didn't rule out running for president himself one day–though he said now isn't "the time that's right for me."
"I may yet run," he said. "There was all this speculation because a whole lot of people said you really ought to think of that. And I appreciated that, and I said publicly that I've been asked by a lot of people to think about that, and that turned into news. Who knew?"
Patrick said he "probably" won't endorse anyone in the 2016 Democratic primary but will "help the nominee if the nominee wants my help."
Sen. Dianne Feinstein, D-California, also expressed some concern about Clinton maintaining a high profile years before the election.
"This is hard for me, because I did talk with her and thought it would be better that she not get out there early, because her favorability was so high that all that could happen in this is go down - because somebody would do the stupid things that Karl Rove has just done,” she said Sunday on CNN’s “State of the Union.”
Rove stirred controversy last week when he brought up Clinton's concussion and blood clot in December 2012 as a potential liability. Clinton’s spokesman and husband, former President Bill Clinton, responded sharply, saying she is "doing great." But Rove’s comments nonetheless renewed questions about whether Hillary Clinton’s health will become an issue in 2016.
Regardless of her timeline, Clinton would be a strong candidate if she decides to run, Feinstein added Sunday.
“We would have someone in the White House who would have a real background in foreign policy - and I think that's critical at this point in the world, with Russia expanding, with Africa becoming real problems from a terror point of view, and on and on and on,” said Feinstein, who chairs the Senate Select Committee on Intelligence.
Gov. Jerry Brown, D-California, also said Sunday that being considered a frontrunner in the early stages has its disadvantages.
"Whether it's a good thing or not, it does carry with it risks. Being a frontrunner is being on a perch that everyone else is going to try to knock you off of," he said on ABC's "This Week."
"So she's there," he continued. "She's got the capacity. But like any frontrunner, she has to be cautious and wise in how she proceeds forward."
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