One issue you'll be faced with is population data in polygons 'assumes' the population is evenly spread across any given polygon. Consequently if your radius/buffer only takes in a portion of a population tract, you will need to know the original area of the census tract, and the area of the portion you have. Then divide the portion area by the original area and then multiply original population by the quotient. Doing that 1K times is ugly.
My suggestion is create a model that will iterate through you points, buffer each one, and then perform a spatial selection on the tracts that the buffer touches; then sum the population for all those tracts and call it good. It's not the most precise calculation but it should get you by.
That should just about do it....