Let's look at what Neil Rackham wrote in SPIN Selling (page 33):
"Closing techniques may increase the chances of making a sale with low-priced products. With expensive products or services, they reduce the chances of making a sale."
Unless you're selling a very low-priced product, don't try to "close the deal" with a first-time visitor to your web site. Instead, close a small deal - a "deal" that costs the "buyer" little or nothing. That deal is a mere stepping stone towards the purchase of your product. Rackham calls this stepping stone an "advance".
Rackham wrote mostly about sales calls, but the same principles apply to web site design. You want to obtain some sort of commitment from the visitor, but you shouldn't expect it to be the placing of an order. Rackham's advice reinforces the notion that your web site should have a call to action, and that it should be realistic.