One problem that Reagan had was that his relationship with Russell meant that while he stood for the New Deal, many on the left of the party hated him when he supported Russell's run in 1952 and his image never recovered from that, you could have him encourage the deal that was being ironed out between Russell and Truman, resulting in a place in a possible Stevenson administration which means that people don't conveniently forget his friendship with JFK, HHH and others.
But that is not the intended effect of this WI. You could have him gain a cold which kills his acting career, where his Democratic sympathies were increased and instead send him to a Republican stronghold in Illinois, he works on a farm maybe and could even succeed Anton Johnson when he died. He'd have hung around Johnson for a while though, he'd gain some conservative Republican credentials and might be able to hold into to that safe seat. Butterflies may get rid of WWII so Roosevelt has more trouble against Wilkie and stands down in 1944, Dewey could lose to however takes over from there, maybe Hull, Wallace or even Kennedy Sr. 1948 will be deadlocked as a result so Reagan, a twelve year congressmen and charismatic young face, could be one of the Taft faction's demands in exchange for endorsing Dewey again. 1948 may go their way.
That good enough?