Well if they have been doing a LOT of sewer work, they MAY have done something so that it now flows slower out of your house. Call them have them look at it. Try to be there when they come by. If you are home and its nothing that they did wrong, maybe ask them if they have a snake to borrow? Or ask one of the workers if he would drop by after hours and do it??We lent them out all the time to the residents.
Ohhh kinda outside the box here, but if you can get them to snake it and they are going to charge you, just ask them if they could put it on your tax bill??
Good luck.