As was well documented during the 2008 banking crisis, the Federal Reserve will buy nearly any securities held by banks during times of banking crisis. In this sense, it's largely irrelevant what kind of securities the banks hold.
What's important then in assessing banks' potential liquidity is the combined value of cash (reserves) and securities the banks have relative to deposit liabilities (the money supply). Today, this ratio is substantially lower than it was on the eve of the banking crisis in September 2008.
So, whatever you've been told about the soundness on U.S. banks, on this measure they are even more unsound today than they were back when Lehman failed. Which suggests the banking crisis could be even greater next time around.