As someone who worked in construction every summer between the ages of 13 and 22, I can tell you right now that your physical condition doesn't mean a fucking thing. Half the fuckers on a job site are probably either heavy smokers or heavy drinkers, or both. That's why these fuckers work in construction.
The only thing you should be worrying about is whether or not you know anything about the kind of work you're doing. You could be Arnold fucking Schwarzenegger, but if you can't use a skilsaw or you don't know what it means when someone tells you to cut an angled piece of wood at 37" to the long side, or if you don't know the difference between a stemwall and a bearing wall, or if you can't read the framing layout on blueprints, or you don't know when and when not to use an A-35 clip, or if you don't know how to square a corner on unlevel ground without a laser level, then the kind of shape you're in doesn't mean a fucking thing. Not one fucking thing.
And you won't have to worry about the kind of shape you're in if you don't know shit about construction work, since you aren't going to get hired anyways. If you somehow get hired on as a laborer, which I can't see happening unless you know the owner since a laborer can get hired at Home Depot for less than what you'll get off your ass for, the shape you're in now is irrelevant. Construction is hard work, but it's not THAT hard, unless you're doing something like a lot of concrete work or something like that. Otherwise, it's the kind of work that a lot of heavy smokers are more than capable of doing everyday for 30 years. I see guys all the time who are in horrendous shape and who work in construction, and they work their asses off, too.
Instead of worrying about what kind of shape you're in, learn how to use a skilsaw without killing yourself, familiarize yourself with a nailgun and an air compressor, get a good sawzall and a good impact gun, buy a hardhat and a decent toolbelt, and start learning how to actually do the work. It's going to be your knowledge and your work ethic that keeps you employed, not your physical shape.