The Marine Corps band played a stirring march in the Rose Parade, as they always do. This one, which I’ve heard since childhood, seems to be polyphonic, with trumpets and higher-pitched woodwinds playing a sort of fanfare, while the bass and contrabass instruments play a repeated, fast phrase that rises and falls. In fact when I heard this as a kid I pictured a ship being lifted and lowered by large waves at sea. I thought it may be “Billboard,” or something like that, but I’m not sure…it might help if there’s a website that plays Sousa music… 
My mother (84) had a very dear friend who would play
Souza marches before dinner every night and make she, her husband and children (all six of them) march around the table before being seated.
I don’t know how familiar you are with Sousa’s work, but typically if Sousa’s playing, it’s either Stars and Stripes Forever, or The Washington Post.
I didn’t see the parade, but listen to The Washington Post, here http://www.dws.org/sousa/mid/washpost.mid and see if that’s it.
Funny, I hear the Liberty Bell more often than not.
What you’re describing sounds a lot like the Billboard March. It’s not one of Sousa’s more famous marches, but it is played somewhat frequently.
If we’re talking about the same Billboard March, then it’s not Sousa’s. John Klohr wrote the Billboard March.
Here’s a MIDI http://www.thejoyboys.com/sound/billb.mid
It’s “Semper Fidelis.” 
:o