The term, "We've run out of ammunition." could have several meanings. I have heard this used in corporate situations to mean we have shot everything at a particular issue and have no more options. Also, Biden has a history of goading enemies into a war as he did with Russia.
More to the point, if he was referring to munitions, what about the hundreds of millions of rounds Obama purchased to corner the market on ammo, drive up the price, and to supplied his own fanciful 'private army' consisting of nationalizing all police forces nationwide, and FBI, CIA, DOJ, NSA, IRS, and DHS which he never managed to bring to fruition. Politically yes, Obama built his own private political army which is alive and well today, DOJ, FBI, IRS. But Obama did not manage to create his own 'armed domestic military army' which is what he really wanted.
Surly all those rounds could be seized and sent to Ukraine, unless Obama's dream is still being considered.