The answer partially depends on whether the garrison in question would be expected to totally stop invaders for an extended period of time, or simply slow them down while taking toll of them. If the former, I doubt Gondor alone could have managed it without leaving the City defenseless.
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Yet (Minas Tirith) was in truth falling year by year into decay; and already it lacked half the men that could have dwelt at ease there.
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ROTK Minas Tirith
So it appears Minas Tirith did not have the manpower on its own.
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And that was all, less than three thousands full told. No more would come.
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ROTK Minas Tirith
The outlying fiefs could initially only supply that small number. Once the southern areas were freed from the threat of the Corsairs, that enabled them to come to the defense and fully man the City, but I don't think they could have done that and guarded a thirty mile long wall at the same time.
With the additional forces of the Rohirrim the Rammas could probably have been garrisoned completely, but in the end I don't see them holding the line indefinitely against Sauron.