I must state the definition again.
Conservatism; The political philosophy adhering strictly to the founding principles of a nation in which one resides.
Now, the Founders were classical liberals meaning this nation's founding principles and founding documents are all classical liberal philosophies. Now that said if you adhere to the founding principles of a nation you reside in, you're a conservative. If you stray away from or reject the founding principles of a nation you reside in, you're a liberal.
All of this said, Classical Liberalism IS modern American Conservatism.