You can drop out of your employer's plan if you are paying part of the cost. Your employer will ask you for a reason. They are looking for a "family status change" or a "life change". These are events like getting married, divorced, having a child, etc. They will ask for this because their plan is set up, assuming that people will stay in it unless they have one of these things happen. If you do not have one of these events going on, you can still drop out by withdrawing your permission to take money from your paycheck to pay for your coverage. This is the "Salary Reduction Agreement". It may be on the same form as your health plan enrollment, but they are two separate things.
If you are required by the Affordable Care Act to have health insurance, you will be faced with the penalty for not having it. As long as your employer's plan costs you less than 9.5% of your income to cover yourself (not your family), then it is considered "affordable" and you would have to pay the penalty.
The penalty may be less than your cost to stay in your employer's plan. In 2014, it is 1 percent of your income or $95 whichever is more. There are other reasons to have health insurance -- like protecting your house and your savings from being taken to pay your hospital bills. Those may seem less compelling when you are struggling to buy groceries. But keep in mind you won't be able to re-join your employer's plan until the next open enrollment. You can't just drop in and out of the plan when you want to.