I currently have a high-deductible healthcare plan with my employer. I have to pay the first $3000 of my medical care, then the plan kicks in at 80%.

To cover this first $3000, i deduct money from my pay check, and put it into a HSA. I have a debit card for this account, and I pay all my medical bills with it.

My question is, is this first $3000 able to be applied toward my un-reimbursed medical expenses?

In general, You can claim a tax deduction for contributions you or someone other than your employer, make to your HSA.However, as long as you deducted the money from your paycheck, Iguess, you can’t claim the money as unreimbursed med exp.
Since the contribution came out on a pre-tax basis, you can already save money on taxes.