Your husband has a very good chance of qualifying for Social Security Disability Insurance benefits, referred to as SSDI, based on his COPD breathing problem. His eligibility for SSDI will depend on the severity of his COPD and whether it prevents him from doing any type of substantial work. Here's how SSDI decides someone's eligibility.
First, your husband will need to have worked and paid Social Security taxes (either paid by his employers or by himself) for a certain number of years. His 25 years of construction work probably more than meets this test, but you should be aware that any time when he was working "off the books" -- without anyone paying Social Security taxes on that income -- will not be counted. At age 51, he would need about seven years of work for which Social Security taxes were paid (give or take a year, depending on when SSDI determines that his disability began).
The next thing SSDI decides is whether his disability prevents him not just from doing the work he usually did but any "substantial gainful work." In other words, it's not just a matter of whether he could continue to do construction work but whether his condition prevents him from doing a substantial amount any other kind of paid work. SSDI decides this question by first looking at the nature of his disability. This they'll do by reviewing his medical records and possibly sending him for further testing (which SSDI pays for) of his breathing. If they determine from his records and this testing that his breathing problem is over a certain standard of severity, they will declare it a "listed impairment" and he will automatically qualify for benefits.
If SSDI determines that his breathing problem is not severe enough to qualify as an automatic listed impairment, then they'll look at his actual ability to perform substantial gainful work. This will include a review of his medical records, the recommendation of his doctor, and also whether he has worked in the recent past. SSDI measures substantial gainful work by whether he could earn more than a specific amount -- in 2010, that amount is $1,000 per month. Since your husband has not worked at all for two years, on doctor's orders, that's a pretty good indication that he's not able to perform substantial gainful employment. Be aware, however, that if he has not even considered any work other than construction, SSDI may need to determine whether he's able to do some other, less physically demanding work which could pay him over that $1,000 monthly amount.
Finally, to qualify for benefits, your husband's condition must be expected to last more than one year. Since it's already lasted over two years, and since COPD is not a condition that generally improves, this shouldn't be a problem for his SSDI benefits eligibility.
All in all, it seems like your husband has a very good chance of qualifying for SSDI benefits right away, and should begin the application process at a local Social Security office as soon as possible. To find out more about disability benefits and about how to begin the application process, you can visit the Social Security website's disability benefits pages.