It could if the US invested enough in bitcoin. Bitcoin has got $1000 before, and if the US government wants to invest, more US citizens will join and bitcoin's price will go sky high. And yes, the US can obliterate their debt.
No, it won't make the price higher because the liquidity will still be low, also what you claiming here is that the US governments should be making up on their citizens and stealing their money, as it's the same thing.
You can't really solve the debt with bitcoin, it's only going to increase it and make the situation even much worse then it is now.
I believe that the US is going to give a fight against the debt by raising the inflation rate ,and at the same time lowering the interest rate.