Opponents also argue that the amendment reinforces income inequality, because women who cannot afford abortions without Medicaid funding will also struggle to afford to raise a child. Ms. Lopez cited a study that found that women who sought an abortion but could not get one were more likely to be living in poverty a year later than women who did get an abortion.

How is it viewed by Americans?

It depends how and whom you ask, but polls tend to show that a slim majority of Americans support it.

A Politico poll in 2016 asked likely voters whether they supported or opposed changing federal policy “in order to allow Medicaid funds to be used to pay for abortions,” and 58 percent said they would oppose that change — in other words, that they supported the Hyde Amendment, though the question did not name it.

A YouGov poll, also in 2016, told respondents that the Hyde Amendment “prohibits federal funds from being used to fund abortions, except in the case of incest, rape or to save the life of the mother,” and found that 55 percent of Americans (not just likely voters) supported it.

A Hart Research Associates poll commissioned by All* Above All in 2015 got a different result with a reframed question, informing respondents: “Under current federal policy, if a woman who is enrolled in the Medicaid health program for low-income people becomes pregnant and decides to carry the pregnancy to term, Medicaid will pay for her pregnancy care and childbirth. Congress currently denies Medicaid coverage for the cost of an abortion.” It then found 56 percent support for a hypothetical bill “that would enable a woman enrolled in Medicaid to have all her pregnancy-related healthcare covered by her insurance, including abortion services.”

Why are the politics changing now?

The shift among top Democrats has been sudden, but among activists, there has been a lot of groundwork.

After the Supreme Court upheld the amendment in 1980 — ruling in Harris v. McRae that while the government could not prohibit abortion, it could use financial incentives to express a preference for childbirth — it became so entrenched in American abortion law that many abortion rights groups stopped trying to repeal it, choosing instead to focus on expanding the exceptions.