I don't believe he should for at least two reasons.
First, the tax dollars are an investment in an forthcoming industry that in future years will be at least as important to the national economy, and hence to keeping our place of economic importance in the world, as computers or aircraft have been in the past. Bio technology will someday be a trillion dollar industry: either for us or the Chinese.
Second, the bill was passed by both houses of Congress, and more accurately represents the will of the people than does Bush's conservative anti-stem cell research base.