Funny you mention that, Henry Clay is the 6th President in my TL, from 1823-1829, and we do see a continuance of national internal improvements. The concept of the "national road" doesn't go away, and by 1910 there are 9 national roads, and once railroads take off, the Federal Bureau of Improvements (which manages said national road network, in addition to several canals) sets up the United States Railway Company and has railways built alongside the existing and new national roads, and also helps to subsidize some private efforts.
If I may make a suggestion: rather than having the United States Railway Company function as both builder and operator for the railroads, have it function more as a builder/maintainer/licensor and franchiser. For example, in OTL the state of Pennsylvania decided the state needed a railroad linking Philadelphia and Pittsburgh, so they got together private capital (with some state funds) to secure financing of the Pennsylvania Railroad, which expanded to serve New York, Washington, Buffalo, Detroit, Chicago, St. Louis and many smaller cities. In your TL, maybe the USRY acts as the conduit for financing and perhaps even builds the initial route, but then licenses or franchises (whatever approach you like) a privately-owned and -financed "Pennsylvania Railroad" to actually operate the route, while continuing to help fund capital improvements and maintenance. The railroad system ITTL would probably have fewer directly competing lines or speculative "railroads to nowhere" like the OTL New York Ontario & Western, possibly not be quite as profitable, but would have a little more long-term stability while avoiding predatory robber baron types (Jay Gould, for example, wouldn't get to "rape" the Erie Railroad and ruin its potential under this scenario).