1948? Where are you getting this? Abortion had been common practice in Moscow until Stalin found that they weren't producing enough good little communists. In California, abortion had been illegal since the 1860s and the law had not changed since 1872, allowing abortion only to save the life of the mother. In 1967, a democrat state lawmaker (Beilenson) pushed to liberalize the laws for just three reasons: to allow abortion in the case of rape, incest, or where the baby might be deformed. (His proposal was backed by the AMA, so I think your 1948 estimate is probably a couple decades off).
Governor Ronald Reagan's first response as "Here's an emotional problem that has so many facets of consideration. It is not only spiritual, but also legal... when does life begin? What right does the unborn life have? What legal right? I'm not prepared to answer now."
In subsequent statements, Reagan took great exception to the portion of the law addressing the possibilty of deformity. "I am satisfied in my own mind we can morally and logically justify liberalized abortions to protect the health of a mother. I cannot justify the taking of an unborn life simply on the supposition that the baby may be born less than a perfect human being... [this kind of thing] wouldn't be much different from what Hitler tried to do."
The deformity provision was dropped shortly thereafter. The final statute permitted abortions in the case of forcible rape, incest, statutory rape if the victim was under 15 years old or if there was a "substantial risk" that continued pregnancy would "gravely impair" the "physical or mental health" of the mother.
The issue then had little to do with "limited government," nor does it now (imo).