Story highlights A veteran's gratitude in Vermont helped change Jane Sanders' mind about her husband running for president

Jane Sanders notes the senator's crossover appeal with Republicans in the Green Mountain State

Washington (CNN) Presidential candidates spend a lot of time pressing the flesh with potential voters in restaurants. Bernie Sanders' White House bid began with a diner coming up to him.

At a Denny's in south Burlington, Vermont, a teary-eyed constituent came over and thanked the senator for his work on veterans' issues, recalled his wife, Jane. She had been reluctant about her husband joining the presidential fray.

"This veteran came by and sat down, and I said after standing up and saying bye to him, 'I guess I give up -- you have to do it,'" Jane O'Meara Sanders said in an interview with CNN's Gloria Borger.

Sanders' odds at claiming the Democratic presidential nomination were long then, and he remains an underdog against front-runner Hillary Clinton. Sanders, in fact, has never even served in elected office as a Democrat. He's been an independent -- a self-described democratic socialist one at that -- through eight years as Burlington mayor, 16 as Vermont's lone House member and nearly nine in the Senate.

But it's Bernie Sanders' potential crossover appeal that convinced Jane he should get into the 2016 race -- and could win.

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