After Round 5
If I have my TPR calculations correct then chess.com article contributor Iryna Zenyuk has the best chance to earn a norm.
WGM Foisor 2364: 6.5/9 for an IM norm (TPR 2479): Needs 3.5 of 4
WGM Abrahamyan 2329: 6.5/9 for an IM norm (TPR 2483): Needs 4 of 4
FM/WIM Melekhina 2242: 5.5/9 for a WGM norm (TPR 2407): Needs 3 of 4
WIM Zenyuk 2224: 5.5/9 for a WGM norm (TPR 2409): Needs 2.5 of 4
Kats 2137: 4.0/9 for a WIM norm (TPR 2295): Needs 3 of 4
After Round 6
If I have my TPR calculations correct then Alisa Melekhina has the best chance to earn a norm.
WGM Abrahamyan 2329: 6.5/9 for an IM norm (TPR 2483): Needs 3 of 3
FM/WIM Melekhina 2242: 5.5/9 for a WGM norm (TPR 2407): Needs 2 of 3
FM/WIM Melekhina 2242: 6.0/9 for an IM norm (TPR 2452): Needs 2.5 of 3
WIM Zenyuk 2224: 5.5/9 for a WGM norm (TPR 2409): Needs 2.5 of 3
Kats 2137: 4.0/9 for a WIM norm (TPR 2295): Needs 3 of 3
2012 05 07 to 2012 05 21
http://www.saintlouischessclub.org/2012-us-championships
Current scores for norms based on the FIDE ratings from March. May be different after the May ratings are published.
Special rules: No foreign federation requirement in a National final. 1.43a
http://www.fide.com/component/handbook/?view=article&id=58
Unknown if some players have already fulfilled norm requirements but do not have the required rating.
Edit 2012 05 10 - May FIDE ratings
IM Zatonskih 2510: N/A (1.45b - Less than 3 GM opponents)
IM Krush 2457: N/A
WGM Baginskaite 2358: 6.5/9 for an IM norm (TPR 2480)
WGM Foisor 2364: 6.5/9 for an IM norm (TPR 2479)
WGM Abrahamyan 2329: 6.5/9 for an IM norm (TPR 2483)
WIM Ni 2228: 5.5/9 for a WGM norm (TPR 2408)
IM Goletiani 2333: N/A
FM/WIM Melekhina 2242: 5.5/9 for a WGM norm (TPR 2407)
WIM Zenyuk 2224: 5.5/9 for a WGM norm (TPR 2409)
Kats 2137: 4.0/9 for a WIM norm (TPR 2295)
I will attempt to update after each round, unless I forget about it.
Official Site Standings http://www.uschesschamps.com/standings-and-games