The Last Child (1971)

"The time: sometime in the future. Mrs. Miller is going to have a baby. But the law says she can't. The law says the world's overpopulated. Run, Mrs. Miller! Run!"

In a badly-overpopulated future, where each couple is only allowed one child and where people over 65 are forbidden medical care under a very draconian set of laws, a young couple, pregnant with their second child (the first died shortly after birth) enlist the help of an elderly former US Senator to help them escape to Canada.