Enough that you don't want to find out the answer.
The U.S. and Russia did renew the New START Treaty in 2021, which has a limit of 1550 deployed nuclear weapons per side, with a slight loophole that a bomber carrying multiple nukes only counts as one.
Economically, Russia has state reserves of roughly $630 billion. The civilian economy has been growing slowly since around 2014, but military spending has increased, and budget surpluses at the federal level have continued. It's probably safe to assume that Russia can afford to keep 1550 nukes in working condition. Part of the goal of these treaties is to avoid senseless spending on excess nukes in an arms race, but if Russia really wanted to save money by spending less on nukes, they likely would have proposed lowering the mutual limit. No point in letting the Americans have 1550 nukes if they could only afford 800, right?
Of course, that also is 1550 deployed nukes. I'm no expert in arms control, but my reading of it would be that you could have more of them in the shed out back, as long as they weren't deployed. Send 1550 of them off in a first strike or response to a first strike, and if anyone's still around afterwards, they can load up more of them to fire later.
Smart leaders like Kim Jong Un are aware that this works both ways, and that if you actually launch them, there will be return fire. So my interpretation of Putin's message is, "don't try anything stupid like trying to use nukes to intervene in Ukraine." In that he would use them in retaliation if they were used first. Plus a little bit of Nixonian madman theory, making you wonder, "would he really use them first?" But like Kim Jong Un, he surely knows that if he used them first, Russia would become a nuclear wasteland. Even if NATO did send troops in to help Ukraine, he'd have to be a fool to use them. Much better to seek a settlement.
But he wants you to not be too sure about that.
