I have two scenarios here on a similar theme, both involving a siege of Nashville, though with the roles reversed. I thought it could be interesting to post them here and see if either could have been a feasible siege.
Scenario 1 - February 1862
Albert Sidney Johnston has been criticized (rightly in my opinion) for his actions before the fall of Fort Donelson. It has been stated that Johnston should have either reinforced the fort with the majority of his forces and gone to take command personally, or should have evacuated the forts to gather his strength later. Instead, Johnston reinforced the garrison with more men then he could afford to lose, but less than could save the fort.
Let's assume Johnston pulls the troops from Donelson, and prepares to defend Nashville. If Davis still gives him Bragg and the Gulf troops, he has about 52-56,000 men against Grant and Buell's combined strength of 60,000 and Foote's flotilla. Who would likely win out?
Scenario 2 - Throughout 1863, James Longstreet had supported moving the balance, if not the entirety, of his corps west to join the Army of Tennessee. Longstreet eventually got with his wish after Gettysburg and Vicksburg, but the victory at Chickamauga was wasted once the Army of the Cumberland was allowed to escape and the Knoxville campaign ended in failure.
Had Longstreet gone west after Chancellorsville, it seems they could have achieved more substantial results. Dealing Rosecrans a defeat before the Tullahoma campaign made capturing Nashville a possibility, as well as relieving pressure off Vicksburg.