Greater Manchester was pretty much blackmailed by the Government to do this - this was the only way that the Government would fund it, ie funding a different scheme and loaning the money out to be paid back by that scheme. £5 billion for Crossrail rather grates compared to everywhere else being forced to get congestion charging schemes and use the money from that to pay back a loan.
That there's the benefit of the improved pt is completely beside the point - that pt should have been paid for (by loan if needbe) directly, rather than forcing Greater Manchester to be guinea pigs for a scheme that has been on and off the shelf for 30 years (going back on for being unworkable, unpopular and just downright stupid). After the carrot of a pt network is in place, then you can start hitting donkeys that don't use it. Then again, it won't help as those who are getting hit with a stick, get hit with a stick because there's no other alternative - people don't want to drive on congested roads, therefore they won't unless they have to.
Also, Trafford and Stockport councils are against it, and Bolton is to hold a referendum on the issue. The other councils (I think Manchester and Rochdale are the big players in this, from what I've read) are forcing a scheme on councils that don't want it. Lovely and undemocratic.