Entering before the date on our letter of invitation

We are American and just applied for a work visa from the consulate in Houston. Our letter of invitation says our arrival date is December 31, but we want to arrive by December 29. When my husband asked the clerk if the work Z would allow us to enter before the date on the LOI, she just half nodded, so he is hesitant to buy plane tickets until we know for sure. I just want to make sure that the entry is valid from the date they issue it. We are supposed to pick up ours on December 26.