You can pay back the cash advance you take against your credit limit over time, just as you would any other purchase you make with your credit card.  Any cash advance you take will be added to your existing balance.  However, this is a very expensive way to borrow money, unless you plan to pay it back immediately.
This is because there is almost always a high fee associated with cash advances on credit cards, and your credit card company will begin assessing interest on the cash advance immediately, usually at a rate above 20 percent.  Unless you are sure you can afford the finance charges that are associated with cash advances, you should probably try to find another way to come up with the cash you need.