Pennys are 97.5% zinc, which currently runs under US $0.73/# (still depressed but up some). There's 181 pennies per pound so that's $0.0040 per penny plus a negligible amount for copper.
That $0.34 was probably from a few months ago when zinc was down around $0.50/#.
The mint claims it costs more than a penny to manufacture a penny, but that's not all metal cost.