In some sense we can think of the essence of a liquidity trap as the public wanting to buy more government bonds than the government is willing to sell.

Traditionally our remedies are:

1) Increasing the amount of bonds the government sells. That is deficit financed spending or tax cuts.

2) Lowering the value of said bonds by promising higher inflation.

However, in theory if some funds are forced to sell Treasuries on a ratings drop this could have the same effect as (2).

The price of Treasuries should not move because they are backstopped against the ZLB. However, some money will move out of Treasuries and into some other asset class, promoting borrowing and lending in that class.