Change default Taxonomy value on form via form alter in D7
It'll be something more along the lines of:

$form['field_mytax_reference'][LANGUAGE_NONE][0]['#default_value'] = $taxTermId;


If the field is a multi-select you would wrap the default value in an array, but there's no need to set a key for it:

$form['field_mytax_reference'][LANGUAGE_NONE][0]['#default_value'] = array($taxTermId);


Have a look at Why is hook_form_alter() so messy? for a bit more info.