Hitching a ride is very likely, but lots of drivers will be picky about the sort of riders that they pick up. Fortunately, at Whitney Portal lots of people look that way. If you have a tiny pack that looks like it will be easy to load into the vehicle, that is a big plus.
Hitchhikers always do better if they have a white sheet of paper with their desired destination written in big letters so that it can be seen by a driver from a hundred feet away. Fold that around a piece of cardboard so that you can display it well.
Lots of hitchers will stand directly at the Whitney Portal trailhead. Others stand just below the overflow parking lot (lower on the hill). Sometimes you can get a ride only to Lone Pine. That is a start. Then on US395, you might pick up another ride heading north.
I met a JMT hiker on the Whitney summit one year, and that was his tenth day from Yosemite Valley. Five hours later, we were at Whitney Portal, and he hitched a ride with me back to the Bay Area that same evening.