The battle of the bulge is superficially similar to the tet offensive in that both were major surprise attacks launched by an enemy that was supposedly on the brink of defeat.
The tet offensive is often described as a propaganda victory for north Vietnam and caused a great deal of political fallout in the United States. But I have never heard any similar discussion of the battle of the bulge's political consequences.
Did The battle of the bulge shake the confidence of US or UK government and civilians? Did opposition parties use it to put pressure on the party in power? Did civilian leaders put more pressure on their commanders or replace them? What was the reaction in Germany and the ussr?
Essentially no political consequences occurred due to the German offensive in December '44.
The confidence of allied military leaders from the army, army group and theatre level was unshaken and civilian political leaders were not either. No commanders were relieved, including the 106th division commander who had two regiments surrender and was personally wounded. Opposition parties didn't make much hay out of it, and in Britain labour was in "national unity" government with the majority party.
There was a minor kerfluffle between British and American army group commanders because of General Montgomery's statements after the danger was over. This was quickly patched up by Ike and Churchill before it could become even remotely serious, and it was rather trivial and petty to start with.
The German reaction is more difficult to gauge, because propaganda was more tightly controlled, and political criticism was constrained (especially in the military) in the wake of the summer attempt on Hitler's life.