This description might be accurate in some situations. In the case of abortion, however, the strict constructionist result Giuliani supposedly favors -- overturning Roe v. Wade -- would mean precisely that "legislatures get to make those decisions."
Giuliani's current stance on the federal Partial Birth Abortion Ban Act, which he says the Supreme Court should uphold, also casts doubt on his allegiance to strict construction. Just as you will have a hard time finding a right to an abortion in the Constitution, you will search in vain for a provision that authorizes Congress to dictate which abortion methods doctors may use.
While introducing new complications to his position, Giuliani has never resolved the longstanding tension between his condemnation of abortion and his insistence that it's a matter of "personal morality" (as he put it in 1989). "I hate it," he recently told Sean Hannity on the Fox News Channel, even while reiterating his support for "a woman's right to choose."
If the reason Giuliani hates abortion is that it involves killing an innocent human being, it's hard to see how abortion can be a matter of strictly personal morality into which the government should not intrude. Perhaps he hates abortion for some other reason -- say, because it's icky. That might explain his newfound support for the "partial birth" abortion ban, but it does not seem like a rational basis for public policy.