It has to do with a different perception of what is commensurate for qualifying as having fulfilled a citizens obligation to the contract.
... maybe? Like, sure, groups vary as to what they think fulfills the social contract, assuming they frame things in that manner to begin with, but that's a pretty empty observation on its own.
The devil's more in the details here, and again, I don't think there's actually a straight answer to be had, exactly.
Especially not on as broad a front as conservative or liberal vis a vis the american political sphere. The positions and contrast you're looking for just aren't particularly consistent, over time, subject, or locality, particularly for the current mess that is stateside conservatism.
Specific subsections of either you might have better luck, assuming they articulate or act like they give a damn what their position regarding a hypothetical social contract is to begin with.