It is possible to run your internet off of a cell phone.
Not particularly fun, but possible.
However, if you're moving to the sticks anyway, you probably won't have much in the way of service. Therefore, a 3G (or even 2.5G) network is unlikely.
Depending on what provider you're with, you could, theoretically, connect to either an HSDPA network (AT&T/GSM), or an EV-DO (Verizon/CDMA) network. Either of these have data rates similar to, but slightly less than, a cable/dsl modem. Also, it obviously depends on signal strength and tower equipment in your area.
To note, the EV-DO network Verizon touts is not really ubiquitous. Similarly, the HSDPA network from AT&T is only rolled out in a few major cities so far. Either option would cost you from 60-100 dollars a month. Finally, you also need a 3G-ready phone. There are several out there (none from SE in the US, unfortunately).
Want to have fun? Look up WIMAX.
Me wanty.
IIRC, T-Mobile has a "hotspot" service that you can get. I *think* that you can use it to install a tiny GSM base station in your house, and then use cell phones with better service.