@PotomacBobUntil recently (post September 11th 2001) the USA did not have a Federal Police Force.
The FBI is an Investigative organization; yes it has a very limited ability to enforce select federal crimes. "Special Agents" specifically means Armed (with at least a pistol) and the authority to arrest. There are not that many FBI agents. DEA, ATF, Treasury Agents, Customs agents & inspectors and US Marshals are also comparatively small agencies with specific narrow functions.
The US Border Patrol (part of ICE) has authority to assist local communities within 50 miles of USA International Borders. (A BORTAC team ended the mass murder in Uvalde, TX.) However, the Border Patrol is spread thin along (mostly) the USA-Mexico border.
Washington DC has a plethora of Federal law Enforcement agencies, or agencies that have "evolved" "law enforcement capabilities" the FDA has multiple SWAT teams (WTF for?!?), the Library of Congress Police, Federal Protective Service, uniformed officers of the Secret Service, Federal Park Police, etc., etc., etc., etc. Mostly located in and around Washington, the District of Columbia; but also NYC, Los Angeles, Chicago, and a dozen to 20 other major cities from Atlanta and Denver to Portland, OR and Seattle.
The TSA (Transportation Security Agency) has grown Massively since 2002! The mouth-breathing people who grope you for the "privilege" of flying commercial; while their comrades piffler your luggage; these low grade thugs are now Armed and DANGEROUS!
Leftists have been agitating for some time for the creation of a Federal Police Force! Meanwhile, castigating Local Law Enforcement agencies and Personnel; Congress has been radically expanding Armed Agents of the Federal Government.
Since the founding of the USA if the Insurrection Act, or other Federal edicts were to be enforced, it has been Presumed that Martial Law would have to be declared. Because the Federal Government only had two options, the "Regular" (standing) Army or Federalizing the Militia of the "several states" because there was no one else. Federal Marshals (actually the Deputy US Marshals they direct) act upon the directives of Federal Judges, are few in number and by Tradition have limited scope.
The State Militias (including "ordinary armed citizens" of the community) now including the National Guard, the State Guards, some states have "Rangers" Naval Militias, etc. were intended as a counterbalance to the "Standing" ("Regular" now called Active Duty) Army (and USMC, etc.)
As per the OP: "For a Story..." the Secretary of Homeland Security and the massive conglomeration of federal agencies could be placed in charge rather than the military and naval forces. It could be argued that, unlike the US Army, the DHS is not subject to Posse Comitatus.
FOZ: Fusion Operations Zones under the control of "Fusion Centers" directed by the Secretary of Homeland Security. Research the DHS Fusion Centers. (in particular whom the various Fusion Centers have target as "threats" I am sure SOL Authors are on the Lists...)