Frances Kissling discusses the background to the Stupak amendment, including the Hyde amendment, in an article at Salon. What made my brain happy was this part:
We started down this road in 1976 when the Hyde Amendment passed and when, in 1980, the Supreme Court upheld the principle that the federal government had the right to enact policies that favored childbirth over abortion by restricting funding for abortion. Most Democrats saw that giving antiabortion taxpayers greater moral standing than women who choose abortion was a political power play. After all, taxpayers don't get any other say in how their taxes are used. Pacifists' dollars support war; anti-bailout Americans saw their taxes go to banks just this year. Except on the issue of abortion, if you want to be a tax resister, the only thing to do is not pay your taxes and go to jail.
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Added later:
Also check out Phila on this topic