“There’s a lot of people, including me, who are hoping that she hangs on to the majority of the money she has because we want to see her run again,” said Michael McNulty, a longtime supporter and confidant of Ms. Giffords…

Veterans on several campaigns in Arizona said Mr. Barber would need to raise as much as $4 million to $6 million by November, noting that Ms. Giffords had one of the most expensive races in the country in 2010. Mr. McNulty said Ms. Giffords would almost certainly donate the maximum allowed by law — $2,000 for each race — to Mr. Barber…

“I think if it’s going to be a long time before she is going to run again, we would love to be able to have that money to elect Democrats in this cycle,” said Jeff Rogers, the chairman of the Pima County Democratic Party. “I think she has shown she could re-raise that rather quickly.”