funding new construction

It's typically a combination of alumnae donations and loans from the University. As far as I know, Nationals doesn't fund any construction. Fo some houses the construction barely raised the cost of dues, these are typically the houses with strong alumnae bases (think DDD, AGD, KD, Chi O, etc). But for other houses the dues are pretty expensive because they relied more heavily on University loans (GPhi, APhi, DG, AXO, etc). I'm a member of a sorority with a new house and my dues are just as expensive as my roommates' who haven't rebuilt yet. It really just depends on the sorority.

For the newer sororities who don't have huge Alabama alumnae bases are dues really enough to cover the multimillion dollar expansions? I guess the loans would be paid back over 15 or 30 years but that still seems a lot...

I'm in a house that the first poster included in the second list and our dues are pretty average. I honestly don't know where the money came from, it's probably in our budget and I just haven't looked, but our dues are definitely normal.

It depends on the house. Those that have been here for many, many years and pledged quota every year....their only expenses over the years have been normal maintenance and redecorating, so they've been stockpiling money for years and years and can cover a good bit of the construction costs.
They also have a lot of alumnae who can contribute, so that will reduce what has to be borrowed. Other houses are newer, have smaller alumnae bases, and have to borrow more.
The "bank" in this case is the university, which is pretty much rolling in money right now thanks to our football team. They're the ones making the loans. Makes good sense for them, because the continue to own the land underneath the houses no matter what, and bigger houses will house more students.
But yes, the houses can make those enormous payments because they have 300 plus members.
What I worry about is when sororities become unpopular and the numbers going through rush drop, and, as in the 1970s, girls resign in droves. And it WILL happen, because the popularity of the Greek system waxes and wanes.