They cannot print "In God We Trust" on bitcoins.
I always thought "In ESCDA and SHA256 We Trust" would be a more appropriate motto.
But seriously, why do you think the government hates bitcoin? I see the government attempting to regulate it, so it doesn't become a method to break existing tax evasion/money laundering laws, but nothing more onerous than what it already applies to existing payment methods or bartering systems. You would still get reported to the IRS if you deposited $10,000 worth of cash to your bank account vs. a transfer of $10,000 of USD from a bitcoin exchange.
Because in a post BTC world, you don't but 10K fiat into your bank account, you pay in BTC