$ ps -aux|grep stringToSearchFor
Obviously, stringToSearchFor is actually the program I was looking for. I even tried redirecting the ps output to a text file and and then used the cat command in a similar fashion:
$ ps -aux>file.txt
$ cat file.txt|grep stringToSearchFor
Looking at file.txt with TextEdit showed that the output of ps is only as wide as there are columns in the current terminal. Resizing the Terminal only goes so far, and trying to change the COLUMNS environment variable doesn't help either. Thus if the string you are looking for would occur off the terminal screen when ps runs, it doesn't exist. So it is very difficult to find!
According to the man file for ps, using the w option forces the output to use 132 columns, which helps little. But if you specify it twice, it forces ps to use as many columns as necessary. Thus long lines are displayed wrapping to the the next line. So if you are looking for lines that you think may be longer than the Terminal's width, use:
$ ps -auxww | grep stringToSearchFor
So using grep as before will now work, as ps will display all of the text for every listed job.
[robg adds: We've shown ps examples before that use the ww setting, but never actually explained it. For you Unix wizards out there, I realize this is a very basic tip. But for those who are still learning their way, it's a useful bit of knowledge...]

