The entire Article 1, Section 8 is details of Congress' rights and duties. "Common defense and general welfare of the United States" in only the vaguest way can be interpreted as specifically "health" in the sense of medical care, provisions for medical research, etc.
Definition: the good fortune, health, happiness, prosperity, etc. of a person, group or organization; well-being: to look after a child's welfare; the physical or moral welfare of society.
Although the word "health" is used in the definition, and the phrase "physical or moral welfare of society" does not abrogate license to the Federal government to inject itself into these matters.
The framers of our Constitution and other originating documents certainly were not prescient. They were, however, fairly wise men who had struggled against what was increasingly becoming oppression in the ruling authority. And they set things in motion with some very firm limitations on government so that future generations could be protected from the same type of oppression. I'm sure that they were fully aware of the wording they were using, and their intentions for using it.
Then, as now, reading anything should always be accompanied with a firm grip on the purpose of the writer(s). Vague wording may be found. The intention was indeed to limit power rather than bestow it, on the government. If vague wording serves that purpose at times, so be it.
Bush is 100% correct to stand against federal funding for this research. If he were standing in the way of the research itself, that would be a different matter altogether. But that is not the case. Abortion, where these embryonic stem cells come from, is a legal act in this country. The courts have found the restrictions on it to be unconstitutional.
I may not agree with that, but it is the law of the land today. If there is the demand for these "harvested" stem cells, and corporations, etc. wish to expend their own research dollars in this direction, so be it. I happen to believe that the whole thing is indeed an effort to shore up an industry that continues to strive for legitimacy. And of course, there is always the money...