Republicans continue to lead the California governor’s race amid a crowded field of Democrats, a new poll commissioned by the state’s Democratic party found, fueling concerns of a conservative win in the famously liberal state.

The party on Tuesday published the results of a large-scale poll of 2,000 likely voters conducted by Evitarus Research that revealed that 16% of participants would back the conservative political commentator Steve Hilton in the upcoming primary, while 14% would support Chad Bianco, the Riverside county sheriff.

Meanwhile, three Democrats were in a dead heat. Congressman Eric Swalwell, former Representative Katie Porter and billionaire environmental activist Tom Steyer each had support from 10% of people surveyed.

The results were somewhat similar to a UC Berkeley Institute of Governmental Studies poll released last week in which Hilton and Bianco were in the lead with 17% and 16% respectively, while Swalwell had 14%, Porter came in with 13% and Steyer had 10%.

“Voters remain largely disengaged and unenthusiastic about the candidates and the election,” Mark DiCamillo, the director of the Berkeley IGS Poll, said in a statement announcing the results of that survey.

In California, the top two candidates in the June primary will advance to the November election regardless of their party affiliation. At least eight Democrats are in the running to replace the outgoing governor, Gavin Newsom, and even candidates with low polling have stayed in the race despite pleas from the California Democratic party for them to drop out.

Earlier this month, Rusty Hicks, the party chair, warned the crowded field could lead to an “unlikely” but “possible” Republican win and urged candidates without a “viable path” in the race to withdraw. Just one candidate did so.

Along with the top three Democrats, the candidates include the former health and human services secretary and state attorney general Xavier Becerra, San Jose’s Mayor Matt Mahan, state schools superintendent Tony Thurmond, former Los Angeles mayor Antonio Villaraigosa and former state controller Betty Yee.

The Evitarus poll showed Becerra, Villaraigosa and Mahan with 3%, Yee with 2% and Thurmond with 1%. But it also suggested voters were not particularly engaged in the race as 24% said they were undecided and not leaning toward any single candidate.

Controversy has sprung up around the race and the Democratic party’s position that candidates with little support should end their campaigns. Thurmond said earlier this month that the political system was rigged and that the party is “essentially telling every candidate of color in the race for governor to drop out”.

The University of Southern California was set to hold a debate featuring Hilton, Bianco, Swalwell, Porter, Steyer and Mahan on Tuesday, but cancelled the event the night before amid criticism for not including any candidates of color.

Hilton described the move as “yet another example of insane Democrat incompetence” and suggested that the Trump administration should suspend federal funding to USC over the cancellation.