The Democratic and Republican leaders in the 2016 White House race are unusually unpopular nationally, polls show, despite their success with voters in their respective parties. Clinton has struggled to generate excitement about her candidacy and assuage voter concerns about her trustworthiness, while Trump fares badly among women and minorities in polls.

Their weaknesses only increase the importance of their vice presidential pick, who could potentially help them rally support in key demographics ahead of the Nov. 8 vote—if each gets their party’s nomination

Hispanic advocacy groups are lobbying Clinton to choose a Hispanic running mate. The person most often mentioned—Julian Castro, the housing and urban development secretary who is one of the party’s rising stars—is opposed by liberal activists who accuse him of favoring Wall Street firms in the sale of distressed mortgages.

Some of the groups have started an online petition against Castro’s candidacy, which has angered the Latino Victory Fund, a nonpartisan advocacy group that has been pushing for a Latino vice-presidential nominee.

“These attacks against Secretary Castro are completely unfounded, short sighted, and only serve to pit us against each other,” said Cristobal Alex, the fund’s president. The U.S. Hispanic Chamber of Commerce has called on Clinton to choose Castro.

For more on Clinton, watch:

Democratic strategist Joe Velasquez, a Clinton supporter, said a Hispanic running mate could make a difference in swing states like Florida, Colorado, Nevada and Virginia, which have large Hispanic populations. Polls show Hispanic voters overwhelmingly dislike Trump, in part because of his comments likening illegal immigrants to criminals.

U.S. Labor Secretary Tom Perez has also been mentioned as a possible Latino pick.

But Clinton’s decision isn’t clear-cut.

Given Trump’s unpopularity with some moderate Republicans, she may want a vice-president who can wrest away some of those voters. Someone like Tim Kaine, a senator from Virginia who personally opposes abortion but supports a woman’s right to choose, or New Jersey Senator Cory Booker, who has close ties to the financial sector.

There was no immediate comment from Castro, Kaine, Perez or Booker.

Clinton though could give a higher priority to winning over liberal democrats, who see her as too pro-Wall Street and have flocked to her rival, Senator Bernie Sanders of Vermont.

Sherrod Brown, a senator from Ohio who is a fierce opponent of global trade deals, and Senator Elizabeth Warren of Massachusetts, a fierce critic of the banking industry, have both been named as possible vice president picks.

Brown and Warren did not respond to requests for comment.

Why Hillary Clinton Should Choose a Republican Vice President

The Clinton campaign confirmed a report in the Boston Globe that Clinton would include at least one woman in any short list of vice presidential candidates to be vetted.

Democratic strategist Chris Kofinis is skeptical that Clinton needs to spend much time appeasing the liberal wing of her party if she wins the nomination.

“As much as people have made out this race between Clinton and Sanders to be an ideological death match, Donald Trump will do more to bring the Democratic Party together than anyone has ever done,” he said.

Trump is viewed unfavorably by 80% of Democrats, according to a recent Reuters/Ipsos tracking poll.

But other Democrats fear the increasingly bitter Clinton-Sanders battle, has fractured the party. Jim Manley, a former top aide to Senate Minority Leader Harry Reid, said Clinton’s pick “has to be viewed through a prism of, among other things, their ability to bring on Sanders voters.”

Reuters/Ipsos polling suggests Clinton would struggle to attract some Sanders voters. When asked what they would do if Clinton was the nominee, 15% of Sanders supporters said they would stay home on Election Day and 16% said they would vote for the Republican nominee. 49% said they would vote for Clinton.

No One Wants to Be Donald Trump’s Vice President

Both the Clinton and Trump campaigns refused to comment on the vice-presidential speculation, saying they remain focused on winning their respective nominating contests.

Clinton holds a commanding lead among the party delegates who will pick the party’s nominee, but Sanders has pledged to keep fighting. Trump may not have the Republican nomination locked down until the summer, if he can beat off challenges by Texas Senator Ted Cruz and Ohio Governor John Kasich, who is running a distant third in the Republican race.

Typically, vice-presidential selections are vetted for weeks after a candidate has emerged as the party’s nominee and are announced shortly before the party conventions in the summer.

Trump’s polarizing candidacy could make his job of finding a running mate more difficult. For much of the campaign season, many in the Republican establishment, along with well-funded political committees, have been looking for ways to keep Trump from winning the Republican nomination.

Trump has stated his preference for an established office-holder rather than a political neophyte like himself, specifically listing Wisconsin Governor Scott Walker, Florida Senator Marco Rubio, and Kasich.

Walker, who has endorsed Cruz, laughed when he was asked about the prospect, but has been noncommittal. Rubio has repeatedly rejected the idea. Kasich last week said there was “zero chance” of his playing second fiddle to Trump, despite mounting speculation that he would be an ideal candidate because of his deep government experience and Ohio’s crucial role as a general election swing state.

A source close to Kasich told Reuters the governor has no interest in working with Trump as the two don’t agree on much.

Cruz, too, said this week he would not be Trump’s running mate, while telling reporters in Hollywood, Florida on Wednesday that “a Trump-Kasich ticket loses to Hillary Clinton.”

For more on Donald Trump, watch: [fortune-brightcove videoid=4855983348001]

Tony Fratto, a Republican strategist, said Trump may be forced to turn to “guys at the end of their careers, not people who believe they have a future. Someone in their last act who has nothing to lose by accepting an offer from Trump.”

That might include New Jersey Governor Chris Christie, who has been one or the few establishment politicians to campaign for Trump, or Florida Governor Rick Scott, who has endorsed Trump. Both are in their final terms in office.

Christie was asked about the prospect in an interview with a New Jersey radio station on Thursday.

“The way I think about these things, you never say ‘never,'” he said.

Other names linked to Trump include former New York Mayor Rudolph Giuliani, Alabama Senator Jeff Sessions, a Trump adviser, and Ben Carson, the retired neurosurgeon and former presidential candidate.

There was no immediate comment from Sessions, Scott and Giuliani. Armstrong Williams, a close adviser to Carson, said the former White House hopeful doesn’t want the slot.

“At this point he has no interest in being in politics … none,” Williams said. “I think Trump is looking for someone with government experience, someone who is more political.”