I'm no constitutional expert, but I'm having a hard time figuring out how the federal government could possibly have the authority this sort of law would require.
Requirements to make and keep records which demonstrate compliance with legal restrictions are a routine and essential part of the enforceability of many laws, so, to the extent that the Constitution explicitly imposes restrictions on the States and explicitly authorizes Congress to enforce those restrictions through "appropriate legislation" (especially in light of the necessary and proper clause), Congressionally-imposed recordkeeping requirements to demonstrate compliance would seem to be within the scope of the Congressional power thus granted.
This is relevant because the 14th Amendment commands that "No State shall [...] deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws" and provides that "The Congress shall have power to enforce, by appropriate legislation, the provisions of this article".
Even with the way the Supreme Court has limited the authorization clause of the 14th Amendment to (unlike identical language elsewhere) only authorize corrective legislation, so that it might not be possible for Congress to impose a general and unconditional requirement, Congress could still impose a requirement on particular states as a consequences of past violation of Constitutional due process or equal protection occurring under the power of those states.
(It could also do it by making it a prerequisite for, say, federal law enforcement assistance funding, or access to federal law enforcement databases, etc. -- and it could do both in parallel, so it would be required both for states found to have past violations for which it serves as a remedy, and for states wishing to federal assistance for law enforcement.)
This is a much more likely to work approach (but not what the petition is asking for).
That said, the political realities of police cameras are going to make this a fight that will not be won on the federal level (especially not in the current environment where getting anything done seems to be seen as treason).
Local laws on the other hand could be easily implemented.
Petitions aren't generally detailed legislative proposals, and their relationship to concrete legislation is similar to the relation between the first draft of requirements for complex computing system and the concrete implementation.
> That said, the political realities of police cameras are going to make this a fight that will not be won on the federal level
Probably not; OTOH, issues like this that make any progress are rarely pushed exclusively in one venue, and even if they aren't won at the federal level, attention there can be a key factor in driving media attention to efforts and driving public awareness. (Plus, heck, the white house petition site has plenty of people petitioning for changes in policies of particular private corporations, so something that's a legitimate public policy issue where the federal government could plausibly do something close to what is requested, even if it would be exactly identical and is unlikely in the current political climate, is actually fairly reasonable.)
Before that, the Supreme Court ruled that growing wheat to feed your own chickens constitutes interstate commerce. https://en.wikipedia.org/w/index.php?title=Wickard_v._Filbur...
If enough politicians wanted the law, the constitutional argument would be of minimal concern.
The federal government cannot rely on the necessary and proper cause to empower it to compel state LEOs to fulfill its federal tasks for it - even temporarily.
The feds can offer "incentive" money, as previous commenters have stated.
Also, the police are going to fight cameras tooth and nail. Major demographics from both parties are going to be mobilized (unions & crime hawks).
The liquor laws were much more sympathetic and even they took a long time for full federal compliance.
The petitions are not bills that people are submitting to the floor of Congress. To say, "well the petition didn't ask for this specific implementation," seems a bit disingenuous. Federal legislation requiring it to receive specific funding would effectively be "federal legislation requiring it" so I'm unsure why you're splitting hairs.
True. They're not much of anything else, either.