A majority of Americans believe that the healthcare system needs fundamental changes or needs to be completely rebuilt and trust Democrats more than Republicans to deliver that change, according to a new poll.

The New York Times/CBS News poll, released Sunday, found that more than eight in 10 said the current system needs either "fundamental changes" or a complete overhaul. More, nearly three quarters of respondents said it is a very serious problem that many Americans do not have health insurance.

And respondents appeared to trust Democrats more than Republicans to reform the system. Nearly six in 10 said Democrats are more likely to improve the healthcare system. Just under two in 10 said the same of Republicans.

The poll also found that respondents are paying close attention to the debate over healthcare. Nearly three quarters said they have read or heard a lot or some about the current proposals.

There appears to be some support for a government run or public option healthcare program. Half said the government would do a better job providing medical coverage than private insurance companies.

Interestingly, while majorities appear to support broad healthcare reform, most appear content with their current coverage. Three quarters said they are either somewhat or very satisfied with the quality of the healthcare they have. Half also said they are satisfied with the cost of their healthcare.