My quick reference shows:
Burnside produced 30,496
Spencer - 64,685
Thus giving Ordnance 95,181 'Carbines'.
No figure on Rifles.
Figure in the fact that Spencer went out of business in 1869 - with assets being purchased by Winchester - and that was essentially the end of issue after the Trapdoor was introduced in 1873.
The Spencer carbine was quickly overshadowed by the lever-action Winchester and with Winchester buying Spencer's equipment - they insured that Spencer wouldn't compete.
The fact is too - that upon adoption - the Army wanted their rifles and carbines to share a commonality - for ammunition and for repair.
They were, after all - the 'new' arm of the United States Army...
Keeping a now-obsolete arm in Service - with almost zero chance of repair parts availability - could have undue consequences.
1873 was the date of adoption of the Trapdoor - and turn-in was fairly rapid.
Spencers continuing service were generally issued to Scouts and the like - not to line troops.
Arguments for and against the Spencer would fuel many a campfire and there were articles written in 'The Army-Navy Journal' so stating their superiority - but you 'have' to factor in the hide-bound attitude of senior Officers and an impecunoius Congress.
When that happens - then as now - the trooper takes a back seat.
Vaya,
Scouts Out!