I don't see much of an issue since we already have 8 lane interstates connecting the vast majority of the cities in this country. The HSR could even connect with the light rail using existing bypasses. We have already emminent domained more space than we need, both inside and outside of the cities.
Easy? No. Easier than continuing to support a broken system of highways that hasn't been revisited in policy since at least the 1970's? Yes.
The double track I was referring to is the light rail that one would use in urban areas. HSR has no need to expand all the way into most city centers.