(CNN) — Measures that would have severely restricted abortion failed Thursday in Nebraska and South Carolina, which both have Republican-controlled legislatures, a reflection of the growing unease among Republicans over the political popularity of strict bans.

In Nebraska, a "Heartbeat Act" would have banned most abortions after six weeks except in cases of rape or incest or to preserve the life of the mother once a "fetal heartbeat" was detected, but it stalled in the legislature. A cloture vote to overcome a filibuster of the bill failed by a vote of 32-15, with two senators abstaining, including Republican state Sen. Merv Riepe — leaving the measure one vote shy of the two-thirds majority needed for full consideration. Riepe, a cosigner to the bill, had proposed an amendment to move the ban to 12 weeks instead of six weeks, but his amendment did not receive a vote Thursday.

On Thursday afternoon, the South Carolina state Senate failed to pass the "Human Life Protection Act," which would have banned abortions in the state, in a 22-21 vote with five women voting against it — including three Republicans. The bill previously passed in the state House and included exceptions for incidents of rape or incest.

In the wake of last year's Supreme Court ruling overturning Roe v. Wade, many Republican-led states have enacted sweeping abortion restrictions. But unpopularity — demonstrated by electoral evidence — over severe restrictions have prompted Republicans to reconsider the political wisdom of enacting near-total bans on the procedure, and House Republicans have recently stepped away from pushing a federal abortion ban.

This story is breaking and will be updated.

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