Entrance into UConn has definitely gotten more challenging in recent years (as had entrance into most nursing programs). For the 2007 entering class of freshman, UConn received something along the lines of 900 applications, of which they sent out between 150-200 acceptances, and they are hoping for a final class number of less then 100.
I can tell you with pretty darn near certainty that I wouldn't have been accepted into the program had I applied right out of high school. Instead I went to UConn majoring in "undecided" (which I was at the time) and transferred in when I realized that nursing was my goal. I'd taken some of my required classes (the math, english, history, biology) and at that point I didn't have any problems with the transfer, as I'd definitely performed far better in college and had a decent (not perfect!) transcript to back me up.
I encourage you to apply. If UConn is what you want, go for it
If you remain concerned about the acceptance process, one suggestion is to call UConn and ask to talk to someone in the admissions office. Ask them what they are looking for in a prospective student, some ways that you can make yourself more appealing to the admissions office, options for if you don't get accepted right away, etc. I liked my time at UConn, and would even consider applying back there in the future for their NP program if I decide to go that route someday.