No. Medicare benefits are tax free; they don’t count as income for determining filing and are not taxed. What’s more, Medicare premiums are tax deductible if you itemize your personal deductions and don’t claim the standard deduction.
For 2007, a high deductible health plan is a health plan with an annual deductible that is not less than $1,100 for self-only coverage or $2,200 for family coverage, and with annual out-of-pocket expenses that do not exceed $5,600 or $11,200, respectively.