No. The president has no part in this. A tie would result in predefined automatic cuts to defense and other discretionary funding.
Supposedly (the Constitution is un-used anymore, so all bets are off on that issue) the Outcome is to be voted upon by Congress, then on to the POTUS who can veto this just like any Legislation. That effectively gives him the deciding vote...likewise, since the Tax Cuts of 2001 are expiring soon, the Republicans will cave on the Tax issue, to save some lobbyists' asses and I fully expect either one or all of the Republican members to be RINO's who'll vote with the Democrats as a "compromise" (i.e., all the spending that the Democrats authorized in the past several years will be kept, except MINOR throw-away items. ALL Union paybacks will be retained, as will Obamacare, the CZARS, the packing of the NLRB, NEA, DHS, etc., etc. It's minor losses for the Dem's in this, and taxes WILL WIND UP BEING RAISED IN THE END, you can count on it.