There are arguments to be made for calling this either a conservative or a liberal document, depending on which aspects of the document you want to look at and how you want to define “liberal” and conservative.
The Constitution is clearly conservative (in our current terms) in the sense that it is meant to ensure that the government cannot be too strong. The system of checks and balances and separation of powers comes out of a strong distrust of government power. This is more of a conservative idea than a liberal one today.
However, the Constitution is also liberal in the sense that it protects many rights that liberals are more likely to care about. For example, the prohibition against unreasonable searches and seizures is something that liberals care more about. We cannot really say, then, that the Constitution is all liberal or all conservative. It clearly has aspects of each.
I agree that a characterization of the Constitution as liberal or conservative can be dependent on how one defines those terms. Additionally, these are not absolute terms, I would say, since what is liberal or conservative in one society can be viewed as such in comparison with other societies. For example, our Constitution, in its provision of power to the people, is wildly liberal in comparison with some monarchies. Also important is to examine the document within the context of its time. Assuming that one defines liberal as providing rights to all individuals that trump the power of the state, the Constitution was an extremely liberal document when it was created and in its subsequent first ten amendments, the Bill of Rights. There was no other nation in the world that created rights such as were afforded to us at the time.
Viewed as a living document, though, which must be frequently interpreted by our courts, the Constitution, in my opinion, is neither liberal nor conservative, since its ongoing interpretations reflect the liberal or conservative bent of the majority of the Supreme Court on any particular issue at any given moment. For example, the present Supreme Court is generally quite liberal in affirming First Amendment rights of free speech. But its interpretations of First Amendment cases regarding the establishment clause are becoming what liberals would consider increasingly conservative. Similarly, interpretations of the Second Amendment are more what we would consider conservative, since American conservatives are all about preserving the right to bear arms, while liberals are all about limiting those rights. Confusingly, voter ID laws are about limiting individual voting rights, and this court has been more prone to permitting restriction on these rights. We call this a conservative position, in spite of the fact that individual rights are being eroded, not conserved. This is the problem with these labels, since in the ordinary meaning of these words, all preservation of the rights set forth in the Constitution, i.e., not diminished, would be considered conservative, and we know very well that politically conservative people in the United States do not agree with some conservation of the rights in the Constitution, for example, an undiminished right to vote, the preservation of privacy in reproduction, or the preservation of the right to not have religion intrude on government actions.