Can I create a button that changes the email notification subject line status?

We have forms to request services. The policy is that we need two weeks advanced notice. In a few cases we will accept urgent request. We need to know in the subject line of the email, we receive, if an urgent request is made. Can we place an URGENT REQUEST button in the form and have it change the subject line in the email?. 

If I understand you properly you mean that you want to allow a button on your form to be able to control the Subject Line of your Email Notification depending on Urgent and Non-Urgent Matters. Is that correct?

The easiest way to do this would be to use a "radio field" and create your Urgent & Non-Urgent Options for the button. You can then add in a {status} tag depending on your field name in the email notification and that can be added to show what sort of urgency it is if any in the subject to simplify it all inside one email notification.

Alternatively, if you want to keep your Urgent and Non-Urgent details separate then a better way to do it in those casetypes would be to create two different email notifications. One will be with the Subject Line for your Urgent Matters. And Two (the other) will be for your Non-Urgent Matters with your Non-Urgent Subject Line.

When you have that set up you can then use Conditional Logic with the use of the Email Logics option to make your form smart to send the correct email with the correct subject matter depending on if it's Urgent or Non-Urgent to notify you based on user-input.