The Ottomans had the men and materiel to besiege Constantinople for an extended period of time, and the Byzantines didn't have much means to bear the siege or relieve it (although the Venetians were en route). Note that Mehmet also pulled off the trick of moving his navy into the Goldern Horn, thus completing the encirclement on sea and on land.

Constantinople would likely have fallen anyways, it was just a matter of how long it would have taken and how many lives would have been lost.