"The real solution here is at the ballot box in 2014," Brophy said.
Republicans have said limiting magazine sizes will drive jobs from the state, and ultimately won't prevent criminals from getting larger magazines in other states.
One Colorado-based manufacturer of ammunition magazines disclosed plans to relocate because of the new restrictions.
Police chiefs in urban areas supported the bills, but some rural county sheriffs opposed the new background checks, arguing the move is unenforceable and endangers Second Amendment rights.
Hickenlooper said law enforcement should try to find common ground.
"This shouldn't be rural versus urban. We are one state," he said.