For Hillary Rodham Clinton, fame has this down side: Even if lots of people like her, many others don’t care for her so much.

Jeb Bush, another presidential aspirant, has a similar problem on the Republican side – only more so.

In polling jargon, it’s the “unfavorables” problem.

Mrs. Clinton is announcing her candidacy today, yet she’s hardly a fresh face to the public. Most Americans already have an opinion of the former secretary of State and first lady.

Some 49 percent of Americans feel favorably about Clinton, but 46 percent had unfavorable views and only 4 percent felt undecided, according to a March ABC News/Washington Post poll. Although different polls give a range of results, that one closely matches the average of recent polling on Clinton, as tracked by Huffington Post.

For Mr. Bush, the challenge of negative opinion is even steeper. The recent polling average is just 33 percent favorable to 49 percent unfavorable. That leaves about 18 percent of Americans undecided about the former Florida governor, who has not yet made his candidacy official.

Perhaps no two people have a stronger shot at getting their party’s nomination and waging viable campaigns for the White House, but for each an important task will be to woo at least some of the voters who are currently skeptical of them or their political families.

The “dynasty” factor has helped put them where they are, but it’s also a hurdle to be overcome.

Where Clinton currently appears hard to assail in her quest for the Democratic nomination, for Mr. Bush the challenge starts within his own party. The questions are, essentially, is he conservative enough and do Republicans want another Bush at the top of their ticket.

Last month, when Bush made his first visit to New Hampshire in the mode of publicly considering a 2016 run, it was an initial step toward appealing for support in that early-primary state.

He showed he cared about fellow party members, participating in a Manchester roundtable that helped to raise $5,400 per couple for Rep. Frank Guinta.

Then he went to a Dover house party hosted by Fergus Cullen, a former chairman of the New Hampshire Republican Party who hasn’t yet committed to backing any particular candidate.

The crowd was modest, in the dozens, but it drew the kind of Republicans whose opinions can influence other primary voters. Many of them were ready to listen to Bush but not to endorse him in a hurry.

Chris Ager of Amherst, NH, said that as a former school board chairman he’s concerned about how the Common Core was pushed on states by the Obama administration. Bush supported Common Core in Florida.

By the end of the night, Mr. Ager came away impressed with Bush: “I got a chance to shake his hand. He has that intangible thing I think that a president has to have.”

On education, Ager still wonders, “Is he going to try to impose his ideas on us, or is he going to let us do what we think is better?... What worked for him in Florida might not work for us.”

While Bush is making his pitch, Clinton has already closed the deal with legions of Democrats.

Nationwide, an impressive 86 percent of Democratic-primary voters say they could support her for the nomination, to only 13 percent saying they could not, in a recent NBC News/Wall Street Journal poll. That’s leagues ahead of other potential Democratic candidates, and a stark contrast with Bush, who garners 49 percent in the “could support” camp and 42 percent who “could not support” among Republican-primary voters.

On the day before Bush’s New Hampshire foray, a crowd of “Ready for Hillary” supporters filled several levels of a Washington, D.C., nightclub for a fund-raising event.

Andy Thorne, an attendee at the event who works at the firm Climate Advisers, said he’s supporting her because “I’m terrified about what the Republicans might do to the environment…. I appreciate the Clinton brand of progressivism mixed with pragmatism.”

Of course, a sizable number of Democrats would like to field a different nominee, maybe one focused more solely on the progressive or liberal policy platform. Some Democratic activists are using “Ready for Boldness” slogan to try to prod Clinton leftward in her positions.

A spate of media coverage about her controversial use of a private email account as secretary of State hasn’t helped her image, either. Clinton’s overall “unfavorable” ratings from Americans have edged up lately.

Her campaign will be working to help Clinton, after more than two decades living in the elite world of the Washington-Manhattan corridor, come off as relatable and revitalized. In the process, she’ll need to fend off attacks from conservatives on her record as Obama’s secretary of State and as a US senator from New York.

The “family connections” issue may cut against Bush more than Clinton. A Christian Science Monitor cover story on political “dynasties” noted that in one January poll, registered voters tended, if anything, to see the presidencies of Bush’s father and brother as a weighing against support for Jeb.

In contrast, 24 percent of registered voters said Bill Clinton’s presidency made them more likely to support Hillary, versus 16 percent who said it made them less likely, in that same ABC News/Washington Post poll.

A bright spot for Bush may be that he’s more of a blank slate to voters than Clinton, even if his family is familiar. But he has a hill to climb to change voters in the “unfavorable” or “no opinion” camps toward a more positive view.

Maybe two hills to climb: first with the Republican base who’ll vote in the primaries, and then in the general election.

In his recent New Hampshire foray, his pitch was that he’s both conservative and – in an implicit dig at rivals to the right – also electable. He told the house-party crowd that his experience in Florida shows, “You can be a conservative, you can do it with joy in your heart … and you can win in a purple state.”

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And he spoke of the need to broaden his party’s appeal: “We have to reach out to people from every walk of life, not with a divisive message but one that is unified, one that says everybody should have a chance to rise up.”

For now, polls of Republican primary voters put Bush at or near the front of the pack, but with plenty of potentially formidable competition.