It is the culmination of a full-scale political transformation by Ms. Sinema, a former social worker and lawyer. The woman now known as a committed centrist ran for the Arizona Legislature nearly two decades ago as a Green Party activist; protested the Iraq war with Code Pink, the left-wing social justice movement; and once warned of the dangers of capitalism and the “almighty dollar.”

Her allies argue that the shift sprang from Ms. Sinema’s desire to play a productive role as a legislator.

“She realized that she could get stuff done working the middle and it had more impact,” said Robert Meza, a Democratic member of Arizona’s statehouse who served with Ms. Sinema during her tenure there from 2004 to 2010. “The left-wing groups, the business community — they started listening more to her. She realized, ‘Hey, I actually have more power in the middle.’”