I'm in the humanities but successfully applied to the States a few years ago (going into the third year of my PhD). Full funding is the rule, rather than the exception, in the US, regardless of discipline (well, excepting professional schools and fine arts qualifications). That said, not all 'full funding' is created equal, and there are some schools where funding is very, very difficult to come by if you are an international student. Regarding the first point: obviously any funding is nice to have, but there are huge discrepancies between a) stipend amounts, b) the work required from you in return for that stipend, and c) the cost of living in various parts of the US...so it's well worth investigating all of those variables for the universities you're interested in, and the areas they are located in. Regarding the second point: the University of California system is constrained by state rules and residency requirements in their support of international students (you will cost them massively more than a US resident, who can become a registered California resident in a year), they're also short of money and so it tends to be REALLY difficult to get funding as an international student outside of science subjects at any UC schools. The University of Washington has a similar problem. Then, there is Chicago and Wisconsin Madison, both of which often give offers with an unfunded first year (apparently partly as a weeding exercise).
So, yeah, in general, funding will be guaranteed for all acceptees, but there are caveats etc. The other thing is that it's just crazy competitive to get accepted. I'm not sure what your discipline is, but Poli Sci and Econ are some of THE most competitive subjects, along with my own discipline (I think the numbers are very similar for these three) - as an example, every school I applied to (a mix of public and private schools, whose rankings on the US news subject tables varied from 2nd to 63rd) had an acceptance rate below 8%. The school I'm attending accepted 4%, and the school I really wanted to go to accepted 1%. It's nuts. To make it worthwhile applying, you really need to apply widely (I applied to 10 places, was accepted to two and waitlisted at one).