WATERTOWN — In a hypothetical race, Gov. Andrew Cuomo still comes out on top when compared to three other big names in New York politics, but he may have some reason to worry in his run for another gubernatorial term.

According to a poll from Zogby Analytics, a Utica-based polling company, Rep. Elise Stefanik would do the best in a speculative race against the governor, although she likely wouldn’t win. Results show 49% of voters would prefer Gov. Cuomo, to 37% who would support Stefanik, R-Schuylerville.

That’s higher than any other potential candidates floated in the survey. Against Democratic state Attorney General Letitia James, 65% of respondents preferred Cuomo to 22% who preferred James, with 13% unsure.

Against Democratic Rep. Alexandria Ocasio-Cortez of New York City, 67% of respondents preferred Gov. Cuomo to 24% who preferred Ocasio-Cortez.

But that doesn’t mean they’re running against Cuomo.

Jonathan Zogby, CEO of Zogby Analytics and son to well-known pollster and founder John J. Zogby, said Stefanik and Ocasio-Cortez, as well as James, were all chosen because they’re well-known names in New York’s political sphere, not because they’re considering running for office.

“We just took some names that are out there in the media right now, names that are kind of popular, but it’s completely speculative,” he said. “Just whatever we thought was interesting at the moment.”

Zogby said the poll is meant to be a reflection of Cuomo’s strengths and weaknesses headed into the 2022 election season, rather than an indicator for the potential support other names included on the list might have if they were to run.

Out of six New York politicians — Stefanik and Ocacio-Cortez, James, Democratic New York City Mayor Bill DeBlasio and Democratic U.S. Sens. Charles Schumer and Kirsten Gillibrand — Cuomo has the best reputation among voters.

More than 60% of poll respondents said they view the governor either very or somewhat favorably, compared to 54% for Schumer and 51% for James.

Rep. Stefanik, the only Republican on the list, came in with the lowest marks. Only 33% of voters said they viewed her favorably, but she was also the least well-known individual on the list, with 29% of respondents saying they weren’t familiar with her.

On job performance, 55% of poll respondents said they think Cuomo has done a good job in office. The job performance question was not posed for any of the other politicians included in the poll.

Statewide, 47% of people believe it’s time for a new governor, compared to 41% who believe Cuomo deserves a fourth term. Among big city respondents, 51% believe Cuomo deserves another term. That flips when you leave the cities — 65% of respondents in rural regions and 51% in the suburbs believe the governor needs to go.

Stefanik performed much better with voters from upstate New York when compared to Cuomo, with 46% of respondents indicating they would support her to 43% saying they would support Cuomo.

Half of voters polled said they blamed Cuomo for thousands of COVID-19 deaths in state nursing homes, an issue on which Stefanik has routinely criticized Cuomo. Even among the Democratic Party, 39% of respondents said they blame Cuomo for the deaths. One-third of voters said they don’t believe the governor holds responsibility for those deaths, and a fifth were unsure.

The governor has been under fire since James’ office released a report nearly two weeks ago that alleged the state Department of Health underreported the number of COVID-19 deaths in nursing homes across the state by about half.

Alex DeGrasse, senior advisor to Stefanik, said Tuesday that the results of the Zogby poll show Cuomo is in the midst of a “political nightmare.”

“A clear plurality of voters want someone new as New York’s governor, and it is clear that despite his embarrassing book and self-centered preening on CNN with his younger brother, Andrew Cuomo has never been in a weaker position politically,” he said. “Cuomo’s gotta go.”

In a statement, Rich Azzopardi, senior advisor to Cuomo, fired back by calling attention to Stefanik’s vote to keep controversial Rep. Marjorie Taylor Greene, R-Ga., on her House committees last week.

“This Q-Anon Trump puppet is trying to distract from the fact that her and the rest of her treason caucus voted to empower a fellow conspiracy nut who said Speaker Pelosi should be shot and 9-11 never happened, and that’s after encouraging a violent insurrection at the Capitol that killed a police officer,” he said. “After seeing those violent videos replayed today at Trump’s impeachment, she is clearly running scared and doing anything to change the subject.”

To conduct their poll, Zogby Analytics reached out to thousands of likely voters across New York via email and asked them to respond to a series of questions with a password-protected and secure invitation.

Zogby said the organization used party registration data and exit polls from 2020 to ensure they poll roughly proportional numbers of Democrats, Republicans and Independents.

For this survey, 810 responses were collected from across the state. The margin of error was plus or minus 3.4%, meaning any figure given could be higher or lower by at most 3.4%.