They will likely pop out. Stick a bit of timber in the gap.
Sounds pretty likely that your calipers are sticking. A good cleaning might do it. Pump the pistons out slightly farther than they typically go. A piece of "timber" is a good idea to prevent them from popping out, but if you're careful, pump slowly and watch, you can do it that way. You may have to hold one piston firm for the other to start moving out. Hot soapy water and a toothbrush- get the pistons spotless so they don't catch.
If that doesn't fix it, or depending on your mileage on the bike, you may want to just go ahead and rebuild the caliper. There are two kits- one with seals that includes pistons and another that just includes the seals. Unless you pistons are marred/rusted, you can probably just polish them up like new.
rocket 3 rear caliper seals | eBay
After that, change the pads if needed and flush with new fluid. Brakes will be like new.
The seals go in a certain direction- make sure you don't reverse them or they will leak. This is a good video on the front caliper, but the process is pretty similar on the rear (easier, only one set of pistons). Right at about 13:00 he describes the orientation of the seals...
With every tire change I do a thorough cleaning of the calipers by removing the pads and extending the pistons so I can clean them. It keeps things working smoothly.
My rear brakes are getting weak and I have this on my "to do" list, as well.
Was this the first ride after putting that car tire on? Maybe need to take it off and put a motorcycle tire back on.
