It helped mostly by pulling the demand forward by creating an incentive to buy now, as opposed to buy later. The price increase came as a consequence of increased number of potential buyers, not the tax credit per se.
I did not offer more to capture the credit, I offered as little as I could to get the house. The credit is just a bonus.
I took my taxpaying coworkers out for a drink when I got it. The remaining $7,750 I put in a savings account.