As I understand it, if the US Govt chose to entirely eradicate bitcoin worldwide the most likely way would be through a 51% attack (please correct me if some other software-based attack might be more effective).
This would be a very expensive way to attack the network, it is unlikely that this attack vector would be used.
Would the US Govt be able to keep a 51% attack secret
An attack isn't an attack unless its doing something bad. If it's doing something bad, then what's being done won't be a secret, although it might be possible to keep secret who is doing the bad thing.
or shift blame to another entity?
Perhaps. Not sure that it matters. The attack is the same regardless of who the perpetrator is.
Would there be signals of a 51% attack or could this occur with no warning?
I suspect that the most likely attack would be a sudden large scale blockchain reorganization going back many weeks or months. You wouldn't know it was being prepared, but the results would be immediately visible once the competing blockchain is broadcast.
How much would a 51% attack cost to implement roughly?
Calculate the total cost to supply enough equipment to be equal to the current total hash power of the entire bitcoin network. Next calculate the total electricity cost of operating that equipment 24 hours a day for the duration that you want to maintain your own alternative blockchain. Next calculate the cost of the salaries of the people you've hired to set it up and keep it running and the maintenance costs of all that hardware. Add it all up, and you've got the total cost. Not sure how much that is, but it seems there are probably more cost efficient attack vectors.
Most importantly - Could any responses be developed within the bitcoin framework or do you see another existing or proposed cryptocurrency that would be safe from a 51% attack?
Perhaps checkpoints or block rejection could be implemented, but its likely that faith in the currency would be lost faster than such solutions could be rolled out.
(for example I hear something about bitcoins being traded "individually"? after such an attack).
I have no idea what that even means.