Democrats are already fighting viciously among themselves over Zohran Mamdani, transgender rights, immigration, Israel and affordability.

Add education to the mix.

The party is debating how to respond to the increasingly muscular Republican push for private-school vouchers — most recently, a provision in President Trump’s budget bill that creates the first national private-school choice program.

States will have the ability to opt in or out, presenting Democratic governors with a difficult decision, and one that competing advocacy groups are trying to influence.

Democrats for Education Reform, a group closely affiliated with veterans of the Obama administration, has become a leading voice urging the party to cross what has long been a red line, and embrace some forms of private-school choice — including the Trump program.

D.F.E.R. has prominent allies, including Arne Duncan, Mr. Obama’s former secretary of education, who is working for the group as a consultant. But its new stance in favor of vouchers is provocative within the party — so much so that two former leaders of the organization have quit and are creating a rival group that will oppose vouchers, while supporting other forms of school choice.

Mr. Trump’s private-school choice program is funded by a federal tax credit, and will offer families of most income levels scholarships that can be used for private-school tuition, tutoring or other education expenses.