Urgency answers "why not later," and that question forms late, after "what is this" and "is it for me" and "does it work." A deadline in the headline, before the visitor knows what is being offered, is pressure without a reason, and it reads as the page shouting before it has introduced itself. The exception is a page for warm traffic that already knows the product, such as a cohort enrolment page for an existing audience, where the date can lead because the visitor's only question is when.
For everyone else, the first mention belongs in the offer section, where the terms are explained and the deadline or capacity is one of them. The second belongs beside the final call to action, as a single line under or next to the button, so the visitor who has finished reading and is deciding gets the one true reason not to put it off.
The visual treatment should match the honesty of the claim. Timers, red badges and pulsing elements are the costume fake urgency wears, and visitors have learned the costume. If your deadline is real, you do not need the costume, and using it anyway makes a true claim look like a false one.