1) Be very careful about staying in valid visa status. You don't want to leave the US then come back only to be told you can't enter. 2) Consult an immigration lawyer (I did). It's not impossible to work in the US on a startup full-time, but there are a few issues you should be aware of (said issues might delay you). Our american friends do definitely have it easier though, as they can drop out of school and not get kicked out of the country :)
The US does actually provide visas (look up E-2 visas) for people who want to set-up businesses in the States (only for citizens of certain countries). But it does seem that these visas stem from a somewhat antiquated view of what starting a company entails (some of the documents required for an E-2 application are incorporation papers, a detailed business plan, bank statements and other financial documents showing where the investment funds are from and how much are involved, business lease, receipts and documentation of equipments, supplies, inventories, contracts and receipts, customer/client list, etc.)
Anyway, best of luck. Like I said, your best source of information is an immigration lawyer. Having said that, I'd also love to hear from other foreigners (real foreigners, not ones that are also American citizens :) who tried to start a startup in the States.
http://www.paulgraham.com/tlbphd.html
I believe some cofounders can still be in grad school, as long as at least one isn't.