“The notion that just because you’re a Democrat” you can take the teachers’ unions for granted “has changed,” said Jim Reed, director of government relations for the Illinois Education Association.

Historically, teachers’ unions have been more proactive than other public sector unions in seeking partners from across the aisle.

But now, as they grapple with a reform agenda backed by hedge funds and large philanthropic donors and championed by the Obama administration as well as some conservative Republicans, the teachers’ unions are navigating a delicate political landscape where they increasingly pursue friends in unlikely places.

“Instead of reaching across the aisle to find support for increased funding for public education,” said Richard W. Hurd, a professor of labor studies at Cornell University, “they are reaching across the aisle for people who are not sold on the idea that charter schools are good, or that testing should be used for all teacher evaluations, or that teachers should lose job security.”