[GK3]

In point of fact, these nations don't much care what happens to Bulgeria (for example) and regard the Baltics as lost causes from day one. 

I understand that Russia is a large country with a significant military.  Yet nothing I've seen in the Ukraine war leads me to believe that Russia would dare invade a NATO country, let alone that Russia would take said NATO county on Day 1.

FWIW, Russia could probably take Latvia in 24 hours. This is not because Latvia wouldn't fight hard, but the country is just too small. It has no strategic depth. Obviously, in "real life" Russia would have to bring forward lots of troops and it wouldn't be a surprise. NATO air would probably prevent such a quick victory. However, I can assure you that NATO most definitely does NOT want to find out how it would go. The tactical situation would be absolutely horrible.

You are correct that right now Russia doesn't dare invade a NATO country such as Romania or Bulgaria because Russia believes 1) the US would fight, and 2) if the US fights, the UK would too. Other NATO countries may not fight (some would) but they probably would let the US transit their territories to do so. The minute the Kremlin believes it probable the US will not fight, the rest of NATO becomes pretty irrelevant. Unfortunately the scenario where Russia believes the US will not fight is easily imagined. This could lead to a major miscalculation on Russia's part or they could in fact be correct.

The US Military OTOH knows that the situation in such an event would be dire. It is difficult for the US to move anything to that part of the world. The transportation system isn't good to begin with, and the Russians would make it even worse by destroying parts of it. The US cannot fight a land war totally supplied from the air. We can't use the Black Sea (Montreaux Convention). If the nearby (mostly NATO) nations don't want to risk involvement (which cannot be ruled out. In fact, it is probable for some of them), we can't bring anything in by land.

So, today you are correct. In a few years, you may not be. My point here is that several of the NATO members are liabilities, not assets. The US military made this quite clear, but political necessity caused them to be overruled. At that time, nobody thought any wars in Europe were even possible anymore, so the fact it was militarily unsound didn't matter.

It seems improbable to me that Russia could put together enough trained manpower and higher end equipment to attempt to invade a NATO country.  Their reported hardware losses in the Ukraine seem to have been significant enough that putting together a large enough invading force would be impossible. I wonder if they can even put together enough resources to even come close to replacing their losses within any reasonable period of time.
In some ways they have done us a favor and helped fire up the NATO Military Industrial Complex so that it would be a bit easier for us to keep up with our hardware losses. Until they invaded Ukraine that might not have been possible. The one part of the Russian military that has escaped significant losses is their Air Force. If the F16's actually arrive at some point and their pilots are capable enough, their air arm might start taking some hits.  
I would also think that they would not Iran to tweak the tiger's tail too far as that might mark the end of their access to their drones. Perhaps they might be trying to influence just how far Iran and its allies carry things vis a vis Israel and the USA.  They need those drones.
With our elections coming up, maybe they are hoping to influence things sufficiently to reduce our support of Ukraine if Putin is playing a longer game. The What If's go on forever.

[GK3]

In point of fact, these nations don't much care what happens to Bulgeria (for example) and regard the Baltics as lost causes from day one. 

I understand that Russia is a large country with a significant military.  Yet nothing I've seen in the Ukraine war leads me to believe that Russia would dare invade a NATO country, let alone that Russia would take said NATO county on Day 1.

FWIW, Russia could probably take Latvia in 24 hours. This is not because Latvia wouldn't fight hard, but the country is just too small. It has no strategic depth. Obviously, in "real life" Russia would have to bring forward lots of troops and it wouldn't be a surprise. NATO air would probably prevent such a quick victory. However, I can assure you that NATO most definitely does NOT want to find out how it would go. The tactical situation would be absolutely horrible.

You are correct that right now Russia doesn't dare invade a NATO country such as Romania or Bulgaria because Russia believes 1) the US would fight, and 2) if the US fights, the UK would too. Other NATO countries may not fight (some would) but they probably would let the US transit their territories to do so. The minute the Kremlin believes it probable the US will not fight, the rest of NATO becomes pretty irrelevant. Unfortunately the scenario where Russia believes the US will not fight is easily imagined. This could lead to a major miscalculation on Russia's part or they could in fact be correct.

The US Military OTOH knows that the situation in such an event would be dire. It is difficult for the US to move anything to that part of the world. The transportation system isn't good to begin with, and the Russians would make it even worse by destroying parts of it. The US cannot fight a land war totally supplied from the air. We can't use the Black Sea (Montreaux Convention). If the nearby (mostly NATO) nations don't want to risk involvement (which cannot be ruled out. In fact, it is probable for some of them), we can't bring anything in by land.

So, today you are correct. In a few years, you may not be. My point here is that several of the NATO members are liabilities, not assets. The US military made this quite clear, but political necessity caused them to be overruled. At that time, nobody thought any wars in Europe were even possible anymore, so the fact it was militarily unsound didn't matter.

It seems improbable to me that Russia could put together enough trained manpower and higher end equipment to attempt to invade a NATO country.  Their reported hardware losses in the Ukraine seem to have been significant enough that putting together a large enough invading force would be impossible. I wonder if they can even put together enough resources to even come close to replacing their losses within any reasonable period of time.
In some ways they have done us a favor and helped fire up the NATO Military Industrial Complex so that it would be a bit easier for us to keep up with our hardware losses. Until they invaded Ukraine that might not have been possible. The one part of the Russian military that has escaped significant losses is their Air Force. If the F16's actually arrive at some point and their pilots are capable enough, their air arm might start taking some hits.  
I would also think that they would not Iran to tweak the tiger's tail too far as that might mark the end of their access to their drones. Perhaps they might be trying to influence just how far Iran and its allies carry things vis a vis Israel and the USA.  They need those drones.
With our elections coming up, maybe they are hoping to influence things sufficiently to reduce our support of Ukraine if Putin is playing a longer game. The What If's go on forever.