Courtesy of YouTube, here's a clip of Christine Ebersole singing "The Revolutionary Costume for Today" at the Drama Desk awards. As you can see, it's a very cute song, but not right as an introduction to the character. When she gets to the part about "staunch women," I finally think, "This is the song you're supposed to be singing!" But that's just a quick bridge, and then it's back to clever rhymes about clothing. Nevertheless, seeing this clip is what made me determined to see the show.
Here's another clip of Christine, not in costume but still very much in character, performing the song "Around the World" at "an ASCAP Foundation Ceremony" (I only know what the YouTube captions tell me). This is a much better marriage of character and song.
If you do go to see this musical (and I do recommend it), you ought to see the movie first. In case you haven't, or if you want to relive the magic, here's a taste of what you're in for: