Lawmakers initially said all children younger than age 17 would make a taxpayer eligible for a $350 rebate check slated to hit mailboxes in the fall of 2014. But children will actually have to be almost 2 years old before that time for their parents to qualify.

Specific details on the rebates finally emerged when the last batch of four budget bills was finalized and introduced late Sunday. The budget, which should be adopted this week, contemplates giving back $375 million in each of the program's three years.

The three-year program starts in 2014, and eligible taxpayers should expect checks around mid-October. Governor Andrew Cuomo as well as the state's 213 legislators are all running for re-election in November of that year.

But to be eligible for the check in 2014, a taxpayer must have a child who was less than 17 years old by December 31, 2012. Taxpayers, either individuals or families qualify if they reported between $40,000 and $300,000 in income in 2012.