George Burns used to say that he married the only woman smart enough to play the dumbest woman in Hollywood. Gracie Allen was undeniably one of the twentieth century's greatest comedians -- arguably her only serious rival for the title of the greatest comedienne is Lucille Ball -- and her ability to play amiable stupidity has a great deal to do with it. With Burns playing straight to her ability to deliver hilarious absurd lines with total sincerity, the duo managed to make the Burns and Allen Show one of the staples of comic radio. It is perhaps a sign of their ability that not only is their sitcom consistently funny, even the product placement for sponsors is funny, as they often had people hawking Swan's Soap or Maxwell House Coffee at the most inappropriate times in the story.
Perhaps the single greatest move they ever made, however, began with a tiny little joke that became an avalanche. Trying to get ratings up, they had Gracie run on the Surprise Party ticket. It was supposed to be two-week gag. It played well enough, though, that Allen just started running with it. Not only were a number of episodes of the Burns and Allen devoted to it, but Allen managed to pull some favors (as she had done for a previous stunt, a search for her 'lost brother') and started appearing in almost all the major comic radio shows of the day, suddenly bursting into the story in random ways to declare her positions issues of the day. (One that people especially remember is her political position on the nation's $43 billion debt: we should be proud of it because it's the biggest in the world. Another: she refused to suggest someone to run for Vice President because she would tolerate no vice at all in her administration. A third: she advocated changing Washington's name from DC to AC, for electrical reasons.)
The campaign picked up momentum; people loved watching Allen spoof the campaigns of FDR and Wendell Willkie. The campaign took on a life of its own; she even held a Surprise Party convention.
It's difficult to pin down all the episodes on which Allen ran the campaign. You can easily find all the episodes that ran on the Burns and Allen Show at the Internet Archive. But other episodes in other series were also involved. At least two of these episodes are worth adding to the cue, both of which have Allen interacting with comic legends of the day.
The first was on Fibber McGee and Molly, "Cleaning the Hall Closet," which also has the distinction of showing the birth of radio's most famous joke, one that passed into a proverb: Fibber McGee's closet. You can listen to it at My Old Radio.
The second was on The Jack Benny Show, "Gracie Allen for President," which you can also listen to at My Old Radio.
NPR's All Things Considered also has a good sum-up of the whole campaign, if you're on a schedule.
Allen also wrote a book connected with the campaign, How to Become President, part of which can be read online:
Presidents are made, not born. That’s a good thing to remember. It’s silly to think that Presidents are born, because very few people are 35 years old at birth, and those who are won’t admit it. So if you’re only 16 don’t be discouraged, because it’s only a phase and there’s nothing wrong with you that you won’t outgrow.