No it should not affect it ........Is it possible that you accidentally got the rotor on the back side of the brake pad ?? , since there are 2 pads , and the rotor goes between , you could have accidentally pushed one of the pads over to the other one and have the rotor in between the caliper and the backside of the pad ...... If you had good brakes before , then it is highly unlikely something just went bad , so I am guessing you inadvertently misaligned something , and that is the issue ...
The brakes did work fine before the tire change correct ???
You might also want to check the fluid and make sure it is full , worst comes to worse , if the rotor is not on the back side of the pad , your next best option would be to bleed the brakes , just make sure to keep adding fluid to keep it up to the top and not let it run dry and get air in the line and see if the pedal firms up that way ..... Hope that helps .....