A three-year surge in anti-abortion measures in more than half the states has altered the landscape for abortion access, with supporters and opponents agreeing that the new restrictions are shutting some clinics, threatening others and making it far more difficult in many regions to obtain the procedure.

Advocates for both sides are preparing for new political campaigns and court battles that could redefine the constitutional limits for curbing the right to abortion set by the 1973 Roe v. Wade decision and later modifications by the Supreme Court.

On Monday, in a clash that is likely to reach the Supreme Court, a federal appeals court in New Orleans will hear arguments on a Texas requirement that abortion doctors have admitting privileges at local hospitals — a measure that caused one-third of the state’s abortion clinics to close, at least temporarily.

Advocates for abortion rights, taking heart from recent signs in Virginia and New Mexico that proposals for strong or intrusive controls may alienate voters, hope to help unseat some Republican governors this year as well as shore up the Democratic majority in the United States Senate.