[cnn-photo-caption image= http://i2.cdn.turner.com/cnn/2009/images/02/17/art.paterson.gi.jpg caption="A majority of voters don't approve of how Paterson handled the appointment of Hillary Clinton's successor."](CNN) - New York Gov. David Paterson could face a bruising primary challenge should current New York Attorney General Andrew Cuomo decide to run.
A new Quinnipiac poll out Tuesday shows the New York governor losing to Cuomo by a 2-1 margin in a primary battle, 55 percent to 23 percent.
The same poll found 45 percent of New Yorkers approve of how Paterson is handling his job as governor, while 41 percent do not.
Should Paterson make it to the general election, the survey also shows him tied with Republican Rudy Giuliani at 43 percent each.
Paterson's low numbers follow controversy over his decision-making process in picking Kirsten Gillibrand as Secretary of State Hillary Clinton's successor in the Senate. Just 35 percent approve of how the process played out while 52 percent disapprove, according to the poll.
The poll surveyed 1,065 New York State registered voters and carries a margin of error of plus or minus 3 percentage points. It was conducted between Febuary 10-15.