Well, what gave us the right to throw out the native inhabitants, drag free labor across the ocean to serve us, and basically set up housekeeping? We do because we can. Might makes right was very big in the 17th and 18th centuries, and really can't be undone at this late date.
Realistically, however, first you have to look at the potential jurisdictions covered by the res. Since there is no geographic or jurisdictional limiter, you are technically looking at not only domestic law enforcement, but also wartime & peacekeeping situations encountered by U.S. Armed forces worldwide, and such other important areas such as CIA covert operations.
In the international context, most of the justification comes from the spurious "we do because we can" more than a specific statutory grant of power. You will find some interesting material in the UCMJ (Uniform Code of Military Justice) covering the conduct of U.S. servicepeople, and potentially other useful material in specific "rules of engagement" promulgated by military brass to deal with particular situations or events. I can see all sorts of Aff's predicated on the rules of engagement for operation of the Abu Gharib prison in Iraq and the prisoners at Guantanamo, etc.
In the domestic context, you look to jurisdiction before the specific underlying justifications. With the actor specified as the USFG, the domestic end of the topic will split into areas where the USFG, specifically the judicial branch, but also Congress in some contexts, controls only the activities and powers of federal law enforcement and courts, as opposed to other areas where the USFG, most notably the federal courts, interpret the U.S. constitution in ways that affect state and local law enforcement. Here, remember that the bill of rights does not confer rights upon individuals so much as it restricts the rights of government. There is considerable debate on the rights and limitations of the sovereign, particularly the question of whether government may do anything it wants, except those things prohibited by law, vs. whether government may do only that which is specifically authorized. For better or worse, the former tends to win out. That being said, start with the supposition that the goverment may hold whoever it wants for whatever reason it wants, and may search wherever it wants for any reason it wants.
With that as a starting point, then look to see where that right is restricted. Provisions of the Constitution itself, governing who may be held to answer for criminal offenses and under what circumstances. This gives you rules governing grand jury presentment and indictment, state procedures for information and preliminary hearings, etc. This also gives you the underpinnings of habeas corpus law - that a person being held must be able to petition a judge of the jurisdiction holding him and obtain an order directing that jurisdiction to demonstrate that the confinement is lawful. Of course, you also have the direct law surrounding the fourth amendment regarding searches and seizures, and the almost gymnastic bending the federal courts have done to create a constitutional concept of "privacy" and similar concepts. Interesting areas may focus on exceptions to the general fourth amendment rule that searches must be predicated upon probable cause in the areas of:
1. Searches incident to arrest (lots of abuse here)
2. "Inventory" searches of a suspect's property subsequent to unrelated arrests.
3. "Stop and Frisk" searches
4. Exceptions governing motor vehicles, travelers using public transportation, entrants to public facilities, etc.
5. New case law granting police the right to stop, temporarily detain and require identification from just about anyone at any time. (personally, I'd love this case area).
6. Laws in many states allowing a person to be held on "reasonable suspicion" or less for periods from 20 hours (as in Missouri) to 48 hours in other states without access to a judge, having availability of bail, or being advised of a charge. There are plenty of incidents where this power is used to harass and intimidate suspects and in some cases keep them away from family or lawyers. Another abuse of this is the serial use of the 20-hour hold to intentionally interfere with a person's life, employment, etc.
7. Similar provisions of Federal law, although the restrictions are much better than most states. The Patriot Act looms somewhat large, though really people will be drawn to that without there really being all that much meat there. The Act lets the government do a lot of abusive things, but they don't fit into the "detain without charge" or "search without probable cause" little holes in the resolution. It would be pretty dangerous to go after the Act as an Aff since it provides so much PIC ground for negs.
There are also some interesting domestic legal squirrels, and one big international squirrel that you might want to look at too:
1. Rights of non-governmental persons and entities to detain and search people. Examples are employers, places of public accomidations like football stadiums, public and private schools, and places like casinos. Specifically, a little sign as you enter Missouri casinos, and those in Nevada, warns that everyone entering is subject to search. Everyone knows that secondary schools can pretty much search you at will, and in many cases, police use this power to have searches conducted by schools and detain suspects when they would legally have no right to do so themselves. Then, to add insult to injury, in many cases, the school can hand the evidence over to police, who may charge and convict a student without regard for how the search was conducted since it was not done by the police.
2. Rights of parents to "detain" and/or search their children.
3. How about the use of the U.S. bully pulpit (economic incentives and sanctions, etc) to coerce foreign governments to improve human rights abuses in their nations?
4. The juvenile justice system, which frequently allows detention and searches otherwise illegal, in the name of identifying "delinquency" and seeking "treatment" for offenders.
5. The posse comitatus act (not sure about spelling) and powers given to bail bondspeople.
6. Immigration law, refugees/asylum seekers, and such (all sorts of ideas here).
7. Mental health - involuntary commitments, etc.
8. From an old NDT topic a few years back, the power of native americans to detain and search under their laws and the extent to which the USFG may control those rights. There was a case back then about how the FBI uses puppet native law enforcement to use tribal laws to gather evidence and detain in ways U.S. law enforcement can't, then package up the case for the feds.
There's plenty more, of course. Hope this helps you. Your actual question is difficult to answer since in most cases, you're just not going to find a formal grant of authority in any source, just limitations of what is an assumed omnibus power to act as sovereign.
If you want more specific information, let me know, and I can do something to put up on Evazon. I'll probably be doing a very big topic analysis with extensive information on all the above and more, to be available in a month or so. I can also pick apart arguments you will hear once the season starts, since debate is notorious for bastardizing the law - you kind of have to in order to fit it in 8 minutes- but I can help.
Chris Cushman, J.D.