The "float" means the number of shares available for trade. If your float is large, the trade in relatively small numbers of stock will not affect stock prices. The phb is under the impression that by buying one stamp at a time, he will not raise the price. This all supposes he thinks of stamps as shares in the post office.
"Float" might mean a couple of things. It could mean that he's "floating" or drifting from pay to pay, making it seem more like a good idea to buy one stamp at a time. He could also be saying that he gets so high at the post office that he's "floating" (I don't know so much about that one, I don't do drugs). He could also be "floating" between women he meets at the post office. Although that's a laugh - PHB flirting?
"Float" is the (perceived) slack time on the non-critical path of a planning. The PHB is obviously on the non-critical path of any project since he cannot contribute anything usefull. Subsequently he fills up his "slack" time with useless tasks... every day!
In this case, float can be taken one of two ways... either he is saying that there are only enough funds to purchase one stamp at a time (possibly because he is so close to budget that he doesn't want to tip the scales)... or he is banking on the possibility of the sudden decline in the cost of stamps relative to the buying power of cash on hand. Either way, it's kinda silly for such a small valued item... especially taking into account the time and expense of going to the post office for each purchase.
I find it slightly ironic that you can now purchase a book of stamps that will still be valid even after the price of new stamps goes up... thus making it more worthwhile to purchase stamps in advance.