US citizens are not permitted to receive the special limited-area visas issued at land borders, to either the Shenzhen Economic Zone or to Zhuhai. This situation has been in effect for some time and there is no indication that the policy will be loosened anytime soon. Do not even try to exit Hong Kong and head across "no mans land" to China as, without a valid visa, the Chinese will likely fine you and then turn you around.
A US passport holder will need a regular Chinese visa of some type (tourist, business) to cross over into the PRC. You can get your visa in advance in the USA (recommended, as you get better terms like 12 months, and multiple entries). Or you can get it in HKG with less generous terms--for this it is best to use an agency like Forever Bright (google them) and let them do the legwork rather than you doing the waiting (often long waiting) at the Chinese mission in Wanchai. Next-day visa service is available for a bit extra.
Regardless of where a US citizen gets the Chinese visa, or terms, it will be $140 or the equivalent in local currency (plus any agent fees plus any Rush processing fees). You'll have to decide if your Shenzhen shopping list justifies getting the visa.