I flew MSP to LAX on 10-13-01, and LAX-MSP on 10-14-01 on NWA. In LAX for my return trip, from the time I got off the National car rental shuttle, until I sat down in the World Club was eight minutes. I used an e-ticket kiosk, and had no checked bags. Smooth in Terminal Two(at 1:30PM on a Sunday).
Terminal One (Southwest) however, was massively crowded, the longest lines I have ever seen. The National bus driver said the estimate was 2,000 people in line. The line snaked back and forth in front of the Terminal. I could see hundreds myself outside in line waiting to get in. The bus driver claimed the line for United was worse. A lady on the bus used her cell phone to call her son who was going to LAS on an earlier flight. She got him on the phone in the Terminal, and was told it took 90 minutes to get inside.
I do not know if the above is typical or even correct (as far as the bus driver's info regarding United, because I got off at T2). It seems to me that you will be ok, even if you have to exit through a zoo at United. Once you get to T2, I hope you find it as open as I did and you can scoot through security (one person in line before me, no wanding of me, nor was my bag opened). The keys are: one carry on bag only and use the e-ticket kiosks. These two precautions will save you massive amounts of time.
I think you will be make it just fine.
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