They can try to argue that Colorado doesn’t have that right/ability, but:

The Constitution also specifies age, residency, and citizenship requirements to run for the House or Senate. Individuals who satisfy those requirements cannot be prohibited from running for office for failing to satisfy other qualifications. States can, however, impose reasonable ballot access restrictions that a candidate must fulfill in order to appear on the ballot, such as submitting a petition signed by a certain number of registered voters. The Supreme Court has aggressively enforced this restriction by invalidating various attempts to impose term limits on Members of Congress. In U.S. Term Limits, Inc. v. Thornton (1995), the Court held that the Elections Clause did not permit a state to refuse to print on the ballot the names of candidates for the U.S. House who already had served three terms there, or the names of candidates for the U.S. Senate who had already served two terms. -Source

And in Term Limits, Inc. v. Thornton, they argued:

the Constitution prohibits States from imposing congressional qualifications additional to those specifically enumerated in its text. Petitioners’ argument that States possess control over qualifications as part of the original powers reserved to them by the Tenth Amendment is rejected for two reasons. First, the power to add qualifications is not within the States’ pre-Tenth Amendment “original powers,” but is a new right arising from the Constitution itself, and thus is not reserved. Second, even if the States possessed some original power in this area, it must be concluded that the Framers intended the Constitution to be the exclusive source of qualifications for Members of Congress, and that the Framers thereby “divested” States of any power to add qualifications.

Well guess what. The disqualification comes straight from the Constitution itself, and has not been restricted or amended by Congress. Ergo it is the only qualification limitation which matters, and a state is well within its authority to enforce it.