Yes. Police do have the right to set up sobriety checkpoints, so long as the checkpoint is constitutional. What makes a checkpoint constitutional? The police officers must treat every car and driver the same. Thus, the police can pull over every single car that goes through the checkpoint, or even every fifth car. The police cannot, however, randomly choose who they can and not pull over based, for example, on the make of the car of the ethnicity of the driver.
Again, going back to the initial stop of the driver – outside of the checkpoint context – a police officer needs reasonable suspicion to pull over the driver. The officer must have a reasonable, articulable suspicion that the driver has or is about to commit a traffic violation, or is committing a equipment violation (such as a busted headlight), or is driving erratically.