Try something like this:
//this hook or general hook_field_widget_form_alter
function hook_field_widget_date_popup_form_alter(&$element, $form_state, &$context){
//only when field is specific name and during node creation form
if ($element['#field_name'] == 'field_date' && !isset($element['#entity']->nid)) {
//if default value is not set, only for second and later elements, when first item value is set
if (!is_array($element['#default_value']) && $element['#delta'] > 0 && isset($form_state['values']['field_date']['und'][$element['#delta']-1]['value'])) {
//set value
$element['#default_value'] = array(
//advance by 24 hours
'value' => $form_state['values']['field_date']['und'][$element['#delta']-1]['value'] + 24 * 3600,
//same timezone
'timezone' => $form_state['values']['field_date']['und'][$element['#delta']-1]['timezone'],
'timezone_db' => 'UTC',
'date_type' => 'datestamp',
);
//if second value (date to) is set (by comparing value and value2)
if ($form_state['values']['field_date']['und'][$element['#delta']-1]['value2'] != $form_state['values']['field_date']['und'][$element['#delta']-1]['value'])
//set and advance second value by 24 hours also
$element['#default_value']['value2'] = $form_state['values']['field_date']['und'][$element['#delta']-1]['value2'] + 24 * 3600;
//#date_items needs to be same as #default_value
$element['#date_items'] = $element['#default_value'];
}
}
}