KLAS reporter Nathan Baca asked Angle about a statement on her website that calls for "transitioning out" Social Security and Medicare programs.
"Why do you want to eliminate [Social Security] for younger folks," he asked.
Angle, who had just returned from a visit to Washington, fired back at him.
"You believe the Harry Reid lie," said Angle, who was campaigning at a Las Vegas restaurant. Angle said she does not believe in eliminating Social Security entirely, but instead transferring the money to private accounts that the government "can't raid."
"You're putting words into my mouth from Harry Reid," a frustrated Angle responded when Baca noted that the stock market downturn would have been devastating to seniors if their savings had been privatized.
"I want you to be very clear on this," she said. "I'm here to save Social Security. Harry Reid is here to bankrupt Social Security."
The former state lawmaker, once considered a long shot for the GOP nomination, easily defeated 12 other candidates in the June 8 primary, thanks in part to help from the Tea Party Express, a national Tea Party organization, and the fiscally conservative organization Club for Growth.
She now faces Senate Majority Leader Harry Reid, believed to be among the must vulnerable Senate Democrats, in November.
Reid recently launched a campaign commercial, in which the announcer says, "Shockingly, Sharron Angle wants to wipe out Social Security." Angle's campaign called that ad a "deception, designed to divert attention from Harry Reid's own failures."
When the KLAS reporter asked about her stated opposition to the Environmental Protection Agency, Angle then replied, "Where are you getting these questions? The issues are not about the EPA. The issues are homes here in Nevada. He is trying to make this a campaign about me. But, where's Harry? Go ask him. Please go ask Harry about the EPA, and why they have failed."
Angle has criticized the EPA for proposing domestic energy regulations that she has said will be "harmful to most sectors of the domestic energy industry and eventually substantially raise the utility bill of every American."
Baca, who then repeatedly tried to ask Angle an additional question as she exited the restaurant, later said the Angle campaign aide called him "an idiot and another term that can't be repeated."
Campaign spokesman Jerry Stacy told CNN the comments did not come from an Angle aide.
"I reviewed the video," he said. "I do not recognize the person in the video that the reporter was talking to. It was not an employee of the campaign."
A Mason-Dixon poll conducted a week before Angle won the primary showed her and Reid statistically tied.