Use Illustrator to fill a path with text

A little option called ‘Envelope Distort’ is what your after. Create your letters in the appropriate font. Make sure the path is the top object and choose the following:

Object > Envelope Distort > Make with top Object

Its best to duplicate the path layer before using the Envolpe Distort function and apply no fill and no stroke. Also, you may want to do a negative offset in order to leave a gap between the letters and the edge of the path:

Choose Object > Path > Offset Path