Not totally the right question: the right question is "does law enforcement have the right to stop your car without probable cause that a crime has occurred?" This is because when your car has been stopped by police, you have been seized for Fourth Amendment purposes. The stop itself triggers the Fourth Amendment, not the search (although there are more Fourth Amendment considerations if a search takes place). The answer to this question is "it depends." Brief, suspicionless seizures at fixed checkpoints have been held constitutional in order to apprehend illegal aliens, detect and remove drunk drivers from the road, and the Supreme Court has implied that these checkpoints would be allowed in order to verify drivers' licenses and registrations--as is the case here--but it has not so squarely held. Each of these are geared at serving permissible highway interests or protection of the border.
On the contrary, the Court has clearly and plainly held that checkpoint programs whose primary purpose was to detect evidence of ordinary criminal wrongdoing are unconstitutional.
"...the Court has clearly and plainly held that checkpoint programs whose primary purpose was to detect evidence of ordinary criminal wrongdoing are unconstitutional."
Which we all know is a load of $#!#, as any cop checkpoints become for the purpose of 'safety' or some other b.s. to skirt that prohibition. Government employees--ESPECIALLY the SCOTUS--are the last people I want protecting me. They protected Randy Weaver's wife and the kids at Waco to death, and protected Elian Gonzalez right back into Castro's arms.