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This appears to be a fairly large receiver, but the caliber looks to be pistol cartridge size. Any help as to the history of the gun and suggestions as to factory caliber would be appreciated. 

Allan

That's a full size Whitney Style II Rolling Block, which were the closest in design to the Remington version. In fact Whitney even marketed them as "Remington Style" in their advertising. 
Whitney began making these after Remington's patent in 1881 and offered them up until 1888 when the company went bankrupt. The Style II were all round top, unlike the first type Whitney-Laidley Style I that were octagon top receivers and made from 1871-1881.

Quite likely it's a .38 Long, or .38 Extra Long. Have you checked the firing pin to see if it's rimfire or centerfire?

Jerry, how in the world do you get your bullets to heal? Those sick buggers I end up with just stay that way until I 'resurrect' them in a new session.

Take a look at .38 long centerfire and .38 Colt long.
The two cartridges are sooo close dimensionally that you should be able to use either as long as your chamber is 1.03 inches long.