This isn't correct though. Only some US states have banned abortions or are set to do so. Others will not do so, and are likely to pass less restrictive abortion laws.
Taking a current example: Switzerland permits elective abortion until 12 weeks whereas New York State permits elective abortion until 24 weeks. Colorado law permits elective abortion until 26 weeks, and medically indicated abortion (e.g., in case of fetal anomalies or genetic disorders) up to 34 weeks.
If you consider the US as a whole, access to abortion is actually more permissive in the US than Switzerland.