Why wouldn't they believe Obama? They're union members. Obama has protected the UAW by nationalizing two auto companies, thrown a trillion toward public sector and construction unions, wants to spend another half a trillion on more union jobs, his NLRB has blocked Boeing from moving to a right-to-work state, and he has promised waivers from Obamacare in every direction for unions. They may be unemployed now, but they're figuring it's their turn next at the trough.
In the end, they'll be screwed, too, but they're not thinking about the end. They're only thinking that without government and their union, they'll have nothing. It's going to take a forceful candidate to convince them that real prosperity comes from a dynamic private economy not a static public economy.
Say what you want, the one who votes their paycheck has better evidence than the one who tallies and mentally collates the historical evidence. But the one (like this crew) who votes his/her imagined paycheck is IMO taking the biggest leap of faith of all.