How long can I leave cooked pot roast sitting out before it needs to be refrigerated?

Cover it and put it back in the oven, on a low temperature (250-Fahrenheit) to keep it hot.

If you put it on the counter it will be okay to eat UNTIL it has cooled off CLOSE to room temperature. But then you will be throwing out whatever is NOT eaten ... no leftovers.

The more it cools down, the more it will be growing bacteria, so it is largely a matter of how MUCH bacteria has grown on it before you eat it.

Now you can kill the bacteria by heating it up (not in the microwave) for half an hour, but that doesn't remove the toxins the bacteria have excreted .. and it is the toxins that mostly make us sick.

So prevention is the key.

General rule of thumb for eating most refrigerable foods left out of the fridge:

No more than 2 hours out of the refrigerator, unless children, seniors or those with compromised immune systems will be eating it -- in which case only one hour.

And then throw out any leftovers.

The refrigerator doesn't stop bacterial growth. It only slows it down. Even the freezer doesn't stop bacterial growth, but grow in the freezer is VERY very slow.

So safety is found in precaution.

It will be fine for an hour or so, but get it refrigerated as soon as you can, just to be safe.

Typically speaking leftovers can be left out for up to 4 hours. 

The two hours suggested by someone else applies to steak.

Let's think about that for a second. If I forget to put my left over steak in the fridge and come back in two hours the powers that be suggest that...hold on

"Cooked steak that has been sitting out for longer than 2 hours (or 1 hour above 90° F) should be discarded."

That is in a commercial setting. There is no way on God's green Earth that I will throw away a $27 Angus steak because it's 2 hours old. 

I have been cooking for about 30 years now both professionally and at home. 

Imo you can leave it out securely wrapped with plastic wrap or foil until your husband arrives.

What about leaving your meat out to rest? When a roast comes out of a 275F oven(started at 350) the juices are in a complete state of disarray due to the heat. Some of the roast will be juicy and flavorfull and some of it will be dry and not so great. Cooks/chefs allow their chicken breast, hamburger, pot roast or any other meat to rest which allows the juices time to settle back into the meat. 

We let the roast beef rest for 30 minutes but it is hot in the kitchen so according to THEM the roast beef will only be good for another 30 minutes. BULL Kahka. 

In your shoes I would leave it out until he arrives.Am I going to put it in the fridge for 3 hours and reheat it from cold? That would significantly change the flavor and if it was cooked to medium, reheating would give you well done... Not what I am looking for.

Wrap it up and leave it out.

Two hours maximum, after which you should place the pot roast in the fridge