ALBANY, N.Y. — For years, Gov. Andrew M. Cuomo and some Democratic leaders have had an antagonistic relationship with the left-leaning Working Families Party, a labor-backed group whose increasing influence and independence have only widened the divide.

So when Mr. Cuomo and state leaders decided this year to expand a public campaign financing commission’s authority — giving it a mandate to rewrite election laws affecting smaller political parties — the independent party’s leaders feared the worst.

On Monday, their concerns were realized: The commission approved a slew of changes that will make it harder for political third parties to survive in New York.