Problem #1: It can kill you
If you have a modern, competently built house, you have a very tight house that does not like to leak air from outside. That is for heating/cooling efficiency. Air is a thing, it's not just magic. If you push air out of a well-sealed house, it will draw a vacuum on the house, just like charging an air compressor tank, but in reverse. The furnace is not designed to do that, so weird things will happen, like carbon monoxide staying in the home and killing you.
Problem #2: It's inefficient.
It is the same problem as portable A/C's, really. Both machines have 2 air streams: a) the house air that is being treated (warmed/cooled)..... and b) the process air the machine need to run on. (A/C makes this air hot; furnace burns it). So we have 4 air ins and outs:
- House air input (raw air from the house, already near correct temp, so reuse it)
- house air output (treated air into the house)
- Process air input (???????)
- Process air exhaust (CANNOT discharge inside the house!!!)
But out of general laziness and cheapness, portable A/C's and 80% gas furnaces only have exhaust pipes for process air output. They steal their process air *input" from inside the house.
This tries to "draw a vacuum" on the house, e.g. Problem #1. But even if your house is old and leaky and the stolen "process air" can easily be replaced by air leakage from outside... there's still another problem. The outside air is exactly what you DON'T want. When you're heating, you don't want ice cold, dry outside air that will have to be heated AND humidified - and this makes drafts! When you're air conditioning, you don't want to draw in hot muggy outside air.
Because those things defeat the purpose. Making the system work even harder at worse efficiency still.
This is why these 1-pipe appliances are stupid.
"I don't like electric heat"
Who can blame you? Electric resistive heat (i.e. just having a bunch of toaster coils to make heat) is the most inefficient thing on earth. It's laughable to even discuss it, unless you're in a place with such a glut of winter power that they give you favorable electric rates (North Carolina, Ontario).
But you say you don't like electric heat? Let's talk about humidification. Humidity is made of the same stuff as heat. Let's suppose the air is dry and you want to add 1 pound of water to the air to make it more humid. Thanks to the latent heat of vaporization, turning 1 pound of tap water from liquid to vapor takes 1200 BTU of heat energy. It's heat. It's the same stuff.
When you're heating your house, replacing this humidity takes more heat. When you're air conditioning, removing this humidity by condensing it takes more cooling.
So you say "no problem, I'll correct the humidity shortage with this humidifier". An electric humidifier, right? Well, that humidifier is also spending 1200 BTU per pound of water, and you're doing that with inefficient electricity. Which is the thing not to do.
So sucking process air from outside is much more costly than you would initially think.
Get the second pipe.
PSA: Heat pumps are vastly cooler than you can imagine.
I saw comments that were like "Heat pump" and "electric heat no way". It's not like that.
Heat pumps are actual, literal magic. They do the thermodynamically impossible: create more heat than they use. Way more. (Well, they're not creating it, they are stealing it thanks to our old frenemy Latent Heat of Vaporization.)
Anyway, here are some technology briefers on the subject:
Early heat pumps had a problem working below freezing weather - and that was a problem in Texas during their cold snap; all the electric emergency heat overloaded the grid.
However first, extended range heat pumps are now available that work at much colder temperatures, and second, ground-sourcing moots the issue.
