In addition, you would be able to sign up only during the general annual enrollment period that runs from Jan. 1 to March 31 each year, and your coverage would not begin until July 1.
The seven-month initial enrollment period begins three months before the month of your 65th birthday and ends three months after that month. (So for example, if you turn 65 in April, your IEP begins Jan. 1 and ends July 31.) The eight-month special enrollment period starts at the end of the month in which you stop working or lose your employer insurance, whichever is first.
Generally, people eligible for Social Security benefits do not pay for Part A. In 2011, the monthly Part B premium, which is deducted from Social Security checks, is $115.40, although for some higher-income earners, the amount is more.
As to your question about taking your Social Security benefits at 66 and continuing to work full time, you are free to do so. Once you have passed your full retirement age, you can earn as much as you wish without any loss of Social Security benefits.
Stan Hinden, a former columnist for the Washington Post, wrote How to Retire Happy: The 12 Most Important Decisions You Must Make Before You Retire. Have a question for the Social Security Mailbox? Check out the archive. If you don't find your answer there, send a query.