ITT Tech will take you as long as they have a spot in the next class (max 15 students per class I think) & you can pass the entrance HESI exam (which is given at no cost to you and you can take it right on their campus.) Tuition is not cheap (they do all the paperwork for you for Pell grants and max out student loans to pay for school, so don't expect to get any money in your pocket) but in 2 years and 3 months you get your RN diploma *NOT* just LPN like most 2 year programs. They also offer an online BSN that you can take after the 2 yr degree if you feel so inclined and want to spend more money. They've got campuses all over the US, but not all of them offer nursing yet.. it's a new thing for them. The school itself has been around forever though, longer than most of the diploma mills popping up everywhere. The reason they have spots open in class is partly due to the high cost and partly because nursing is new to the school.. word hasn't gotten out yet they they are starting to teach nursing.
I'm pretty sure their admissions policy has nothing to do with a nursing shortage and everything to do with them making money, but I am OK with that.