A siege of an entire mountain (Erebor) brings to mind the 8-month Crusader siege of Antioch during the First Crusade. There werne't enough men to meffectively close off even the city, a mountain, with dwarf engineering technology able to send out scouting groups, raiding/harassing parties etc. at their own initiative would be highly difficult (at least, without a dragon patrolling around Erebor
). There would presumably be enormous food and storage prepared (again, not unlike castle preparations in the Middle east with large water retaining stone pits). And even Thorin and Company were prepared to put up resistance on a hastily build wall against the combined elf/man army.