Formula that looks at the text and month and then adds the correct numbers

[scrim]

What I have is the following information,
\1

I am trying to figure out a formula that adds up only the totals for John Smith in January. I think I need to combine an IF with a SUMIF but I can't get it to work. What formula will work?

So far I've worked out:

=SUMIF(C2:C7,">="&DATE(2011,1,1),B2:B7)-SUMIF(C2:C7,">"&DATE(2011,1,31),B2:B7)

But I can't get to the next level that would look at my employees before looking at the dates