Set default value of field in a field group
I was able to spend some more time on this and figured out that the field group was not where I should be changing the value in the form. 

I am using the field group multiple module so the value is not being set at the field or the field group. If using devel, look for something like 'fgm_node_YOURNODE_form_group_YOURGROUPNAME' where YOURNODE will be the name of your content type and YOURGROUPNAME will be the name you gave to your field group. I'm assuming 'fgm' is short for field group multiple. 

You will have to travese 'fgm_node_YOURNODE_form_group_YOURGROUPNAME' to find the specific field within the field group multiple that you want to set the default value. 

Example:

$form['fgm_node_YOURNODE_form_group_YOURGROUPNAME']['fields']['items'][0][field_YOURFIELD']['und'][0]['value']['#default_value'] = t('Some text');


My form alter code works now.