President Trump receives praise after signing a bill in June 2017 that makes it easier to fire Department of Veterans Affairs employees. Officials from the Koch-backed Concerned Veterans for America are among those in attendance. (Jabin Botsford/The Washington Post)

As Veterans Affairs Secretary David Shulkin battled last month to keep his job, his fate hinged in part on a once-obscure advocacy group backed by billionaire industrialists Charles and David Koch.

In the end, Shulkin’s refusal to pursue greater outsourcing of health care for veterans — the top priority of the Koch-backed Concerned Veterans for America — further alienated him from the group’s allies in the Trump administration and contributed to his ouster, according to officials familiar with the situation.