You may be able to go temporarily as a student though if you've got the $$$'s to pay for school at international student fees.
If you already have a bachelors and want to go to the US for grad school (masters or PhD), then it doesn't have to cost much. I got accepted into a fully-funded PhD program in the US and I only had to pay for the visa and the flights - the university paid my tuition and my funding/living costs came from being a TA/RA (it was about $12,000 a year for teaching 20 hours a week in term-time and doing research in the summer).
However, if you wanted to do a bachelors in the US, you're talking about needing maybe $30,000+ per year in tuition and living costs (the university I was at charged $17,000 per year for tuition, but other schools, like Harvard, charge more than $40,000 per year).