SWAT teams are police, but they're still loaded for bear, and they're the primary counter-terrorism units inside the US. They have armored vehicles, automatic weapons, shotguns, flashbang grenades, helicopters for insertion, snipers, whatever they need for the task at hand. SWAT teams are equipped and trained to deal with hostage crises, domestic terrorism, urban guerrillas, gang warfare, mafia, bank robberies, clocktower snipers, shooting sprees, anything with a small number of very dangerous people. They're what enables the police to never request military support unless there's a complete breakdown in law and order. SWAT teams also have access to police-grade chemical weapons that the military don't due to international treaties.
The military has counter-terrorism units that aren't called SWAT teams, but they aren't used domestically because the Posse Comitatus Act prohibits the army from being deployed for domestic law enforcement unless authorized by an act of Congress, and the Department of Defense voluntarily extends that prohibition to all branches of the military. The exception is the National Guard, which can be called up by State governments, but that's still reserved for cases where sheer manpower is an issue, such as rioting or restoring order after a natural disaster. The National Guard are part-time citizen-soldiers that have day jobs they have to be pulled away from, and they actually modify their guns to disable automatic fire when acting as a police force. Their purpose is to be a show of force, to communicate that the army is here to restore order, to bolster police manpower, and to provide tanks and planes if needed.
It is possible for the government to send in an elite military team like the Navy Seals or another special forces unit, it just would need to be authorized by Congress. It would be interesting to have an actual event in LCS where Congress votes to authorize deploying elite military forces against the LCS.