Contractors receiving a 1099-MISC are expected to report these earnings on a Schedule C and you would be subject to self-employment taxes, which is 15.3%, half of which is deductible for income tax purposes. In addition, you can claim deduction for any expenses you incurred while performing your consulting work, perhaps even for a home office. There is no withholdiing on 1099 income unless you do not furnish a Social Security or employer identification number. You will instead be expected to make estimated tax payment or, alternately increase withholding on other income like Social Security benefits.
In order to avoid an estimated tax penalty, you will need to have paid in 100% of your last year's taxes or 90% of your current years taxes in four equal quarterly installments or through withholding. If you expect most of your income to come in later in the year, you an annualize your income so your quarterly required payments can vary based upon when you received your income. However, as long have made payments based upon last year's tax, you can wait to pay any balance due April 15, 2016 without any estimated tax penalty.
I do not know how much your 1099 income will be or anything else about your tax return, so I can't know exactly how it will affect your taxes (in terms of numbers). As an additional service I can put together a projection of your 2015 tax based upon the year-to-date income, deductions, and payment as well as last year's tax.
Finally, as long as you have reached full retirement age, self-employment income will not reduce your Social Security benefits at all.
I hope this answers your question. Please let me know if I can clarify anything or answer any additional questions. Thanks, Jonathan