"The Congress shall have Power To ... provide for the ... general Welfare of the United States" seems broad enough to support the constitutionality of Federal research grants.
The Framers were divided between two possible interpretations of the general welfare clause: one proposed by Madison, and another by Hamilton. Neither interpretation seems to justify giving money to universities.
Madison argued that the general welfare clause was not an indepdent source of power. Rather, the term "general welfare" was (according to him) merely a synonym for the enumerated powers considered collectively. Thus, the general welfare clause did not confer any new authority, but merely functioned as a limitation on the power to tax. Under this interpretation, it is clear that federal research grants are not constitutionally permissible.
Hamilton argued that the general welfare clause was indeed an indepdent source of federal authority, over and above the enumerated powers. However, he did not believe that the spending power was unlimited. He argued: "The only qualification of the generallity of the Phrase in question, which seems to be admissible, is this--That the object to which an appropriation of money is to be made be General and not local." Arguably, education is a purely local rather than "General" (i.e., federal) issue.
I agree, but I would not characterize one who receives money as a "state actor." I was under the impression that this term is normally reserved for government itself, and not applied to private entities who are not acting on the government's behalf.