The deal allowed Zardari and Benazir Bhutto, his wife and a former prime minister, to return from self-exile without facing corruption charges.
But the NRO has been branded unconstitutional and the debate over its legitimacy has received a great deal of coverage in Pakistani media.
The amnesty covers more than 8,000 officials and civil rights activists argue that it was unjust to help so many politicians escape prosecution for alleged wrongdoing.
As president, Zardari, who has denied a slew of corruption claims against him, enjoys general immunity from prosecution, but the Supreme Court could choose to challenge his eligibility for the post if the amnesty is declared illegal.
Legal and political analysts are divided on whether this is likely, and most expect the process to take several months to run its course.
The debate comes as Pakistan's army battles Taliban fighters in its tribal regions and the potential crisis is a cause for concern in the US, which wants Pakistan to remain focused on its anti-Taliban campaign.