I would do a spatial join between your point data and US Counties.

If you do not have US Counties, you can download the 2014 Counties here.

Then, add both layers into your map.

Click Vector -> Data Management Tools -> Join attributes by location

Set the target vector layer to your points.

Set the join vector layer to your counties.

Choose to take attributes of first located feature.

Rename your output shapefile.

Select to keep all records (so you don't lose any records).

Click Ok.
 
Once complete, your point output will have the county information added to it.

I would do a spatial join between your point data and US Counties.

If you do not have US Counties, you can download the 2014 Counties here.

Then, add both layers into your map.

Click Vector -> Data Management Tools -> Join attributes by location

Set the target vector layer to your points.

Set the join vector layer to your counties.

Choose to take attributes of first located feature.

Rename your output shapefile.

Select to keep all records (so you don't lose any records).

Click Ok.

Once complete, your point output will have the county information added to it.

Keep in mind:

• The projections of your data
• All fields from the counties will come over, but you can delete them once the process is completed
• As reference, here is a tutorial doing a very similar process, except it chooses to aggregate a field rather than just joining the data