That is, how many actual people with guns could the Feds put on the street? This might be hard to answer because publicly available stats would only give the total number of employees, which would include the janitors and the 60 year old file clerks. Specificly NOT counting the armed forces or the intelligence agenices, you still have the FBI, the DEA, the Treasury, the Secret Service, the BATF, the Federal Marshalls, the IRS, and I don’t know who else.
Don’t forget the Border Patrol and the Federal Bureau of Prisons. They’re two of the largest uniformed services in the federal government (both are bigger than the FBI).
Just cause a fed has a gun does not mean there is any ‘armed strength’ there. 
YMMV
The Federal Law Enforcement Training CEnter (FLETC) trains more than 80 federal agencies. A quick look at their partner list shows some federal agencies you would never have imagined at first glance that have law enforcement capabilities.
It’s important to note, though, that a lot of the training that goes on at FLETC has nothing to do with firearms. They have a lot of different modules geared toward teaching proper investigative procedure, legal issues, and other more administrative aspects of law enforcement. I’d imagine that much of the agency staff that gets sent to FLETC never touch a gun.
And why exactly do you want to know this, Lumpy? Are you planning something special?
Well, my uncle Arthur used to have a saying: “Shoot 'em all and let God sort 'em out.” Unfortunately, one day put his theory into practice. It took 75 federal marshalls to bring him down. Now let’s never speak of him again.
I was just musing about the Founding Fathers and their loathing of standing armies; and it occured to me that quite apart from the extraordinary step of calling out military troops, the federal government has an enormous armed strength just to carry out it’s police powers. I imagine that if for some political or legal reason the feds couldn’t or wouldn’t resort to the military to impose the federal will, they could still in a pinch put down about twenty Wacos simultaneously.