There are 2 ways to see the number of opt-outs following a text blast: 

1) Go to Reports > Keyword Summary > set your date range for the date of the broadcast and click the search icon > then, look to the Opt-Out Column related to the campaign.

2) Go to Reports > Mobile Summary > set your date range for the date of the broadcast and click the search icon > then, look to the Contacts Overview and Message Overview sections for "Opted Out" and "Stops".

Alternatively, if you're interested in seeing the actual mobile numbers that opted-out:

3) Go to Reports > Received Log > select the keyword filter, exact match, then pick your campaign from the drop down menu > set your date range for the date of the broadcast and click the search icon > it will produce a list of all contacts that replied to the campaign on the specific date, including opt-outs.