I've got the same error, started 3 hours ago, on my SGS2. I re-authenticated, deleted my application password, created a new one, it authenticated properly, but the Market was still unable to log-in, even when gtalk and gmail were working as expected. When trying to access the Market, I've got:
Authentication required. Please log into your Google account.
I rebooted, navigated different sites and everything except the market seems to work. I'll update with findings.
[ACTUAL SET] NEXUS 4, JB 4.2.2 CUSTOM STOCK, TWRP
[HISTORY] PALM OS:M500/M515/T3/TX/TREO680// SYMBIAN:N95/N97(NOKIA)
ANDROID:MILESTONE(MOTO)/NEXUS ONE(HTC), ATRIX (MOTO), SGS2, GALAXY NOTE, SGS3 (SAMSUNG) ONE X (HTC)