Flake made the comments last week in response to a question at an event in Payson, Ariz. The local newspaper, the Payson Roundup, first noted the response on Friday.
In doing so, Flake came out alongside hardcore Tea Party candidates who favor the repeal of the 17th Amendment, which was adopted in 1913 to let voters pick their senators. But even some Tea Party candidates have said repealing the amendment would be a step too far for them.
On Monday, Flake's campaign spokesman Andrew Wilder told TPM in an email that the congressman isn't outright calling for repeal. His position represents little more than a fantasy.
"It's important to note that Jeff understands that the ship has sailed," Wilder said, "and he has not introduced or supported bills on this issue."
But Wilder also sent over what he said was a verbatim transcript of the answer Flake gave to the crowd in Payson. The answer makes it clear that Flake would prefer to take the power away from voters and give it to his fellow politicians.
"I should just mention, on the 17th Amendment, I think it's better as it reinforces the notion of federalism to have senators appointed by state legislatures," Flake said, according to his campaign. "Having said that, I'm under no illusion that you'll ever go back because you have 100 senators who have been elected who would worry that they wouldn't be appointed and so I think we've probably crossed that Rubicon."
The idea of repealing the 17th Amendment has been floating around in conservative circles for years. Rep. Louie Gohmert (R-Texas) has even introduced legislation to do so.
The statements come at a time when polls show Flake cruising to an easy primary victory but eyeing a tight general election against former U.S. Surgeon General Richard Carmona, a Democrat. The PollTracker Average shows Flake on top of Carmona by just 5.3 percent.