Virginia

First of all, ALWAYS wear a Personal Flotation Device (PFD)

This is highly dependent on how the vessel is aground. If you are aground on the rocks or on the sand and there is a danger due to high waves, a hull breach, flooding or injury, the US Coast Guard is going to do everything humanly possible to assist those persons in distress. There is a point though, where if there is a high probability that it will jeopardize the lives of the boat crews or helicopter crew, they may have to wait till the situation stabilizes. They will exhaust every possible option first.

If you are aground and in no danger, they may broadcast marine assistance request for other boaters, commercial tow or wait for you to re-float, depending on the location, assets available and severity of the grounding. The US Coast Guard is not required to salvage your vessel, their responsibility is to the persons in distress. You can always contact the US Coast Guard on channel 16 (International Hailing and Distress). The first four questions you will be asked. 1. Position (lat and long or geographical), 2.) Nature of distress (aground, sinking, fire, manoverboard..) 3.) Description of your vessel 4.) And is everyone wearing a life jacket (pfd). Please refer to the link provided in the related link section.
The coast guard is required to assist when a person is in distress. They are not required to salvage your boat.