score:5
First lets get some semantics out of the way. You will never officially be given a "3 month" stay on VWP. The maximum is 90 days. The difference is only a day or two, but it matters because even a 1 day overstay is an overstay!
Immigration officials most definitely have the ability to limit your stay to less than the normal 3 months that you would get under the VWP. What's more, you have no right to appeal their decision to do so - one of the conditions of using the VWP is that you give up any right of appeal to their decision.
So the issue here is obviously how long a stay you were officially given. There are two places that the official length of stay is recorded - one is in your passport (presumably 90 days), and what is entered in their computer system. Two these entries should be the same, but it's possible that the immigration officer made a mistake and put the wrong date on your passport.
Thankfully you can check the date in the computer by going to http://www.cbp.gov/i94
If the date on your electronic I94 matches the date on your passport, then you are officially good to stay for 90 days. It is certainly possible that the officer made a note in your record that you were to leave within 2 months, which could cause you issues the next time you enter the US - but legally for this trip at least you're good to stay 90 days.
If the date in the computer is different, then you've got a problem. In this case, they officer has given you 60 days, but apparently stamped your passport with the wrong date. If this is the case then you've probably got 3 options :