The obstacle cited most among all respondents was saving enough for a down payment at 29%. Next was housing supply constraints at 27%, followed by access to credit and financing at 22% and personal debt at 19%.

And among African-Americans and Asians a similar trend played out. The highest share of respondents in these two groups cited a lack of down payment or savings as the main barrier to homeownership, with 33% of African-Americans and 32% of Asians.

But among Hispanics, a third of respondents chose access to credit and financing as the biggest obstacle. And 31% of non-Hispanic whites, meanwhile, selected constrained housing supply as the most challenging barrier.

"With record high rents and only about a third of the state's households able to afford to buy a median-priced home, the dream of owning a home in California is evaporating," CAR President Pat Zicarelli said in a news release Thursday. "It's even more discouraging for prospective ethnic homebuyers who must face greater obstacles to scrape together a down payment or obtain credit and financing."

But there was some stronger agreement across racial and ethnic lines on other issues. For example, 70% of poll respondents looking to buy a home said that they want the current presidential candidates to address housing affordability during their campaigns.

Additionally, 84% of respondents said that owning a home "gives them a greater sense of well-being and control," the CAR noted in the release, and 72% cited homeownership as part of their retirement strategy.