Unfortunately, Bank of America no longer offers the Quick Payment service that they used to have, and they announced two years ago that they'd be bringing it to an end back in March 2012.
When the original service was put to an end, they replaced it with something called Online Bill Pay, which is still available today. It doesn't give the Same Day guarantee, but they say that many bills and transfers can be made as early as the next working day.
And you also have the added convenience of being able to choose if you want it to be a one-off payment or a regular one, scheduling when to send the money out in the future.
Their website notes that if you've got any questions about the Quick Payment service, you can ring up the freephone number that's printed on your statements to discuss it with one of their advisers.