The ZLB per se doesn’t matter it is that the Fed targets interest rates and that bank reserves wash with t-bills. Thus anything that attempts to increase the demand for t-bills in fact increases excess reserves. Funds flow straight through the t-bill market into excess reserves.
In addition attempts to save through buying government securities simply results in a monetary contraction and running up a deficit simply results in a monetary expansion.
Now outside the ZLB the Fed could simply cut in response to this but at the ZLB it cannot. That’s the difference. At the ZLB the Fed cannot – using standard monetary policy – cut the link between what happens in the T-Bill market and the effective money supply.
It could using non-standard monetary policy but that’s the whole issue in a way.