Not much is known about uranium reserves, as the amount of exploration has been far less than for oil, etc. Also, if the most easily-recovered uranium became more scarce and price increased, there is a lot more than can be economically recovered. Uranium is fairly common stuff--about as common as tin or zinc. Today, the fuel cost for electricity from nuclear plants amounts to 2 cents per kwh (about 1/2 the price of coal), so even if the price of uranium doubled it would still not be prohibitively expensive.
And, of course, if we decide to use breeder reactors, we'll have fuel for a very long time (millions of years).
Yes, I know breeder reactors have their own set of issues (particularly the proliferation potential of the increased storage and shipment of Pu), but these problems aren't technical ones.
The info above and more:
Freedom For Fission- finding the fuel
And this, from a more impartial site:
"Uranium is an abundant natural resource that is found all over the world. At current rates of use, uranium resources could last more than 500 years. (A process called "breeding," which converts uranium into plutonium-an even better fuel--could extend uranium reserves for millions of years.)"