Washington (CNN) New York Gov. Andrew Cuomo holds a double-digit lead over his Democratic primary challenger, Cynthia Nixon, according to a new poll. But his grip on the race could be loosening.

Fifty percent of registered Democrats said they would back Cuomo for a third term as 28% support Nixon, according to a Quinnipiac University poll out Wednesday.

Cuomo is 22 points ahead in this latest survey, the governor's narrowest lead in the contest across three statewide polls released since Nixon announced her candidacy. It's down nearly 10 points since last month -- though the results, coming from different polls with different interviewers, may not be directly comparable.

Before she announced her run , Nixon was trailing Cuomo by a whopping 47 points, in a mid-March Siena College poll.

The "Sex and the City" actress and education activist still faces an uphill battle to unseat Cuomo, who has strong support from men and women but Nixon fares better among very liberal Democrat voters.

Last month Nixon received a big progressive endorsement from the small but influential New York Working Families Party . The coalition of labor unions, a number of which left the party in protest of its decision, and progressive activist groups broke its alliance with Cuomo and decided to endorse Nixon. Working Families Party leaders accused Cuomo at the time of threatening labor leaders who sided with Nixon, a charge the governor's campaign has denied.

The Democratic primary election in New York is September 13.

The Quinnipiac poll out Wednesday was conducted April 26 to May 1 among 1,076 New York voters, with a margin of error of plus or minus 3.7 percentage points. Voters were reached via cellphone or landline.