S.T.
Did you get to sit in on the speech therapy? When my son began speech at this age I sat in on the therapy for the first few weeks - and then after a few months I needed to do so again. Speech therapy is work - the therapist has to keep him on task, and has to teach him things are not natural to him. Some therapists are VERY good, and have a natural way with kids and find ways to persuade them to do difficult things. Others are not as good and find it awkward to get kids to do stuff and are more rigid in their approach.
Remeber he's only been on the planet for 3 years. He's still so little and he wants to be with his mommy - he doesn't want to do things that are difficult -he wants to play. He is 3...
I would try to sit in on speech, bring a magazine & sit quietly in the corner jsut to observe the dynamics. Do not get involved in the "class" in any way unless the therapist asks you to. If you think she is not a good match for your son ask to have a different one for him and see if that makes a difference. It may or may not.
Set up expectations in advance. Tell him that you know he can go to pre-school, babysitter, etc. and have fun. Tell him that you are so proud of him for beginning speech therapy - that he must feel like such a big boy. Give him postivie reinforcement. Maybe a small chart with stickers, a sticker for each time he goes to preschool without a fuss, or to speech, etc. When he's got one row of stickers (5 boxes in a row?) tell him he gets a special something. I used to use Rescue Heros for my son - he loved them. So after a row of stickers we'd go pick out a rescue hero. after a week or two discontinue the sticker/rewards, but continue to give him hugs, tell him how proud you are of him, how you knew he could do it, etc.
This can also be the beginning of a new developmental stage too. Whenever my kids began some new level of developement, or before a growth spurt, there would be a teary, shy, tired, cranky period. We had teary relapses plently of times over the years. My daughter had a very tough 2nd grade - although 1st grade was a breeze. Who knows. Just love him and remind him that you ALWAYS come back - that there is no way you would ever leave him because you love him so much.
Good luck!