Answer: No, they cannot. And if they do, and find contraband (like a gun), the court will throw it out. Chris Marcus and his friends were having a party inside and outside of his open garage/rec room. The police responded to a noise disturbance and saw Marcus smoking a joint in his driveway. When he saw the cops, Marcus walked back inside his garage/rec room. The police ran into his garage, tackled him and removed a gun from his waistband. He was convicted of being a felon in possession of a firearm.

The Florida Supreme Court overturned his conviction, in Florida v. Marcus, finding that the exigent circumstances of hot pursuit do not justify a warrantless entry into someone's home in order to search them or the home. In other words, if you're engaged in a minor crime (like smoking weed), and walk into your home, the police can arrest you - it just doesn't give them the right to conduct a search of you or your home. And yes, your open garage is considered part of your home, protected by the Fourth Amendment of the Constitution from unlawful searches and seizures.