For months, Democrats have worked to challenge attorney Robert F. Kennedy Jr.’s ballot access in key states across the country. With Vice President Harris in the race, though, it appears Mr. Kennedy might play more of a spoiler for the GOP.

Next week, Mr. Kennedy is due at a Harrisburg court for a hearing related to a Democratic effort to deny his campaign ballot access in Pennsylvania in November.

When the race was between Presidents Trump and Biden, Mr. Kennedy’s candidacy threatened to have a significant spoiler effect for Democrats, especially in close states. Now, though, it appears that Mr. Kennedy may play the spoiler for Republicans more than Democrats, calling into question whether Democrats will want to redouble their efforts to keep him off the ballot.

A July New York Times and Siena College poll found that in a multi-candidate race, Ms. Harris leads Trump 44 percent to 43 percent, with Mr. Kennedy taking 5 percent of the vote.

“By self reported party identification, Mr. Kennedy enjoyed the support of 3 percent of Democrats, 3 percent of Republicans, and 10 percent of Independents,” the survey said.

However, when the pollster asked political leaners and third-party voters to choose between Trump and Ms. Harris, just 21 percent of voters who previously said they planned to vote for Mr. Kennedy said they would support Ms. Harris, while 50 percent of Mr. Kennedy’s supporters broke for Trump.

The Times and Siena College survey polled 1,142 likely voters between July 22 and July 24, with a margin of error of plus or minus 3.3 points.

The trend appears to have held since mid-July.

A more recent survey from RMG Research for the Napolitan Institute found that in a multi-candidate field Trump leads 46 percent to 45 percent nationally, with 5 percent backing Mr. Kennedy.

Under this scenario, Mr. Kennedy wins 2 percent of the GOP vote, 16 percent of GOP leaners, 20 percent of independents, 11 percent of Democratic learners, and 2 percent of the Democratic vote.

When asked to choose to between Trump and Ms. Harris, Trump wins back 1 percent of the GOP vote and 14 percent of the GOP leaners who previously supported Mr. Kennedy. Trump also wins 3 percent of self-identified Democratic leaners and 1 percent of Democrats, and 6 percent of independents.

Ms. Harris on the other hand wins back 2 points of the Democratic vote, 8 percent of Democratic leaners, 8 percent of independents, 2 percent of GOP leaners, and 1 percent of Republicans.

The upshot here is that a larger proportion of Republican-leaning voters, who might otherwise vote for Trump, are planning to support Mr. Kennedy.

The RMG survey polled 2,708 likely voters and was conducted between August 12 and August 14.

Another survey, from Fox News and conducted by Beacon Research and Shaw and Company Research, found that in a multi-candidate race, Trump and Ms. Harris are tied at 45 percent support, with Mr. Kennedy taking 6 percent of the vote.

When third-party and undecided voters are asked to choose between Trump and Ms. Harris, however, Trump leads 50 percent to 49 percent.

Mr. Kennedy’s supporters included 4 percent of voters who supported Ms. Harris and 7 percent of the voters who supported Trump when asked to choose between just two candidates.

The Fox News poll was conducted between August 9 and August 12 and had a margin of error of plus or minus 3 points. With all surveys, the margin of error in individual polling crosstabs will be higher than in topline results.

With Mr. Kennedy appearing to have more appeal to Trump voters than Ms. Harris supporters, it’s not clear whether the Democrats’ challenges to Mr. Kennedy’s ballot access makes sense electorally.

As it stands, Mr. Kennedy claims to have ballot access in 45 states, though only 15 states have confirmed that he will appear on ballots. The most consequential of these states are Michigan, Nevada, and North Carolina. 

Mr. Kennedy is also on the ballot in Texas and Florida, two states in which Democrats have competed in recent history, though it’s not clear that they will be competitive in 2024.

Mr. Kennedy has also reportedly sought a meeting with Ms. Harris, with the Washington Post reporting that he wanted to exchange a Cabinet position for an endorsement, an offer that was said to be rejected.

“I think it is a strategic mistake for them. That’s my perspective,” Mr. Kennedy told the Post. “I think they ought to be looking at every opportunity. I think it is going to be a very close race.”

Mr. Kennedy later walked back this comment, posting on X: “I have no plans to endorse Kamala Harris for President. I do have a plan to defeat her.”

Last month, Trump reportedly did meet with Mr. Kennedy, who was then seeking his endorsement, though Mr. Kennedy denies that he has any plans to drop out of the race.