NYS Town Law regarding budgets

    §  109.  Final  revision  and  adoption of budget. 1. After the public
  hearing, the town  board  may  further  change,  alter  and  revise  the
  preliminary budget, subject, however, to the requirements of subdivision
  one of section one hundred seven of this chapter.
    2.  The  preliminary  budget  as submitted or amended shall be finally
  adopted by resolution of the town board not later than the twentieth day
  of November, except that in towns in Westchester and Monroe counties not
  later than the twentieth day of  December.  The  preliminary  budget  as
  adopted  shall be known as the annual budget for the town for the fiscal
  year beginning on the first day of January next succeeding, and it shall
  be entered in the minutes of the town board.
    3. Upon the adoption of the resolution required by  this  section  the
  amounts  proposed to be appropriated shall thereupon be appropriated. In
  the event that the town board shall fail to adopt a  budget  as  of  the
  twentieth  day  of  November,  or  in  towns  in  Westchester and Monroe
  counties as of the twentieth day of December,  the  preliminary  budget,
  with such changes, alterations and revisions, if any, as shall have been
  made  by  the  town  board,  shall constitute the budget for the ensuing
  fiscal year.

--------------------------------------------------------------------------

In the case of the failed Fishkill budget this is what is important.

The preliminary budget is the responsibility of the entire town board. Ergo, 

the entire town board is responsible for the 53% tax increase.