Among the reasons DOJ wants to avoid getting a warrant: it wants police to be able to use the device at the beginning of an investigation, to help them establish probable cause (which is needed for search warrants, wiretaps and indictments.)
The court of appeals’ decision, which will require law enforcement officers to obtain a warrant before placing a GPS device on a vehicle if the device will be used for a “prolonged” time period, has created uncertainty surrounding the use of an important law enforcement tool. Although in some investigations the government could establish probable cause and obtain a warrant before using a GPS device, federal law enforcement agencies frequently use tracking devices early in investigations, before suspicions have ripened into probable Cause. The court of appeals’ decision prevents law enforcement officers from using GPS devices in an effort to gather information to establish probable cause, which will seriously impede the government’s ability to investigate leads and tips on drug trafficking, terrorism, and other crimes.
The Justice Department is concerned that requiring a warrant and probable cause for GPS devices may have a spillover effect on other law enforcement techniques that don't currently require a warrant: "Pen registers, repeated trash pulls, aggregation of financial data, and prolonged visual surveillance" among them.
DOJ says the issue is ripe for the Supreme Court because there's a split in the circuits, as the 7th and 9th Circuits have ruled prolonged GPS monitoring of a vehicle is not a search within the meaning of the Fourth Amendment.
While the petition mentions a few state court rulings in its favor, I didn't see any mention of rulings by courts in Delaware, New York, Oregon and Massachusetts that have found GPS devices do require warrants.
The Court of Appeals got it right when it ruled:
Society recognizes Jones‘s expectation of privacy in his movements over the course of a month as reasonable, and the use of the GPS device to monitor those movements defeated that reasonable expectation. As we have discussed, prolonged GPS monitoring reveals an intimate picture of the subject‘s life that he expects no one to have — short perhaps of his spouse. The intrusion such monitoring makes into the subject‘s private affairs stands in stark contrast to the relatively brief intrusion at issue in Knotts; indeed it exceeds the intrusions occasioned by every police practice the Supreme Court has deemed a search under Katz....
The individual expectation of privacy has become the exception, rather than the rule. Like license plate readers, toll transponders and video cameras with face-recognition technology, with GPS, law enforcement is turning us into "an always-on, surveillance society."
The unfortunate notion that electronic surveillance of cars and people is acceptable and routine has spilled over to the business and the public. Here's a company hawking its GPS devices for businesses to put on employees' vehicles to track their movements and "idling time." Or these ads for GPS devices to track your children:
Introducing the new Amber Alert GPS technology that was designed to answer the all-important question, “Where Is My Child?”
...With information being sent every 60 seconds you’ll be able to see the location of your child wherever they are. Their movement is presented on a live map showing where they are, where they have been and even where they may be headed.
...Only your imagination limits the uses of this amazing and efficient new GPS child locator technology.
What a slippery slope this is.