"Some people might ask, 'Hey Ron, what took you so long?'" he said. "I don’t rush into things, but once I make a decision, I stick with it for the long haul."

Four Republicans are competing in the primary for the special election, but all the other potential Democratic candidates cleared the field out of deference to Barber and to Giffords, who endorsed her former staffer and encouraged her supporters to donate to his campaign. Giffords's support — plus the endorsements Barber has picked up from local GOP officials — has helped him fashion himself as the heir apparent to the popular, centrist former congresswoman.

But at least four Democrats have announced plans to run in the regular election, leading to a possible primary contest in the fall between those Democrats and Barber, who may or may not be an incumbent member of Congress come June.

State Sen. Paula Aboud (D) and state Rep. Matt Heinz (D) had also launched bids for the full term. Both said Barber's announcement didn't change their intentions.

"I'm supporting Ron to replace Gabby for the rest of the term," Aboud told The Hill. "But I'm moving forward, and I am focused on the new district in the fall."

Another Democratic candidate, Arizona state Rep. Steve Farley is expected to bow out of the primary to avoid challenging Barber. Both Barber and Farley have enlisted former Giffords staffers to run their congressional campaigns, making it highly unlikely the two would engage in a primary fight.

The special election is being held under the current congressional lines, while the regular election in the fall will take place under a new map that improves the district slightly for Democrats.

- This post was updated at 10:16 p.m.