Newly installed Archbishop Timothy Dolan of the Archdiocese of New York said he would challenge any efforts legalizing same-sex marriages in New York.
The bill also appears to lack the necessary support in the state Senate.
Paterson has seen a same-sex bill fail before in Albany. In 2007, when Paterson was lieutenant governor, then-Gov. Eliot Spitzer's gay-union bill passed the Assembly. It died in the then-Republican-controlled Senate.
Democrats are now in control of the Senate, but passage of Paterson's bill could still prove difficult.
Paterson ally Senate Majority Leader Malcolm Smith (D-St. Albans) said he hasn't secured enough votes in favor of the measure.