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Barr wouldn't elaborate on who exactly had contacted Carmona, but added that thus far he hadn't been in touch with national Democrats about a potential run. He added that Arizona Democrats believe that Carmona at the top of the ticket could boost other statewide Democratic candidates in 2014, when Arizona will see a state attorney general, secretary of state and state treasurer race, as well as the gubernatorial race, play out.

Carmona posted a surprisingly strong showing for a Democrat running in a red state against then-Rep. Jeff FlakeJeffrey (Jeff) Lane FlakeAuthorizing military force is necessary, but insufficient Republicans jockey for position on immigration McCain, Flake warn against 'politically-motivated penalties' for Canadian defense firm MORE (R), who ultimately toppled him. But Flake only won by 3 percentage points, while the Republican presidential nominee won the state by 9 percentage points, indicating Carmona had high bipartisan appeal.

He's still months away from a decision, but Barr said Carmona's staff is working to remain prepared in case the Democrat does decide to launch a bid.

"His staff is doing everything we can to keep the infrastructure ready in case he chooses to run," he said.