The differences between conservatives and classical liberals can be settled after modern liberal nihilism has been knocked six feet under. While that remains a clear and present danger to the survival of civilization, any theoretical contrast between the former is entirely moot.
And that is why, despite the differences between traditional conservatives adn classical liberals, we remain in alliance. It is an alliance against progressivism.
Some of teh Founders were classical liberals. Some would be considered more conservative. They divided into parties on those lines. Today, they would all be in the same party.