Can the cops enter your home without a warrant if you refuse to let them in?

It depends on the particular facts whether or not the police can enter without a warrant.

For example, if the police are in hot pursuit chasing a suspect who may have entered your house, the police could enter without a warrant and search the premises.

Another example would be the police searching your house incident to an arrest.  They arrest someone at your house or on your property outside your house.

Another example would be if the police spotted contraband in plain view such as drug paraphernalia sitting next to a window, they could enter without a warrant because by the time they got a search warrant and returned the contraband may be gone.

Another example would be exigent circumstances.  This would be an emergency situation where the police have a reasonable belief that there is something in your house that may endanger the police or members of the public such as explosives.  They could enter without a warrant because by the time they left and returned with a search warrant, the explosives or some other dangerous item may have caused an injury or otherwise endangered the safety of others.