Tie for first might be worse than wild card.

How to determine playoff tiebreakers
MLB.com | September 8th, 2015

If one game is needed to break a tie for a playoff berth between two teams, it will be played on the Monday after the scheduled end to the regular season, hosted by the team that won the season series against the other. That applies to determining a division championship whether or not the losing team would still qualify as a Wild Card.

Home-field advantage is determined first by head-to-head records, then by the higher winning percentage in intradivision games. If a further tiebreaker is needed, it's the best winning percentage in the last half of intraleague games.
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That's from the bowels of mlb.com and required a nifty Google search to find.  It gets much worse as various scenarios up to four teams being tied are explained.

The New York Yankees are three games behind the first place Toronto Blue Jays in the American Conference (AC) Eastern division with 17 scheduled games to play, including three between these two teams in Toronto.  The Blue Jays have already won the season series with 11 wins and 5 losses against the Yankees, so a tiebreaker game between them would be played in Toronto on Monday Oct. 5.

The Yankees regular season ends with a 3:05 PM start on Sunday Oct. 4 in Baltimore, so they would need to travel to Toronto to play the next day.

Aren't all pitchers shut down on their rest days? Monday, September 14, 2015

In 2014 the Yankees started Masahiro Tanaka on four days rest in 8 of 20 starts.  In 2015 that has shrunk to 4 of 22.
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Tanaka just beat the Blue Jays in Toronto on Sunday, Sept. 13 and he's scheduled to pitch Friday Sept. 18 against the Mets in Citi Field on four days rest so that he can come back on four days rest and pitch against the Blue Jays again on Wednesday Sept. 23 in the last scheduled game of the season between the teams.  That will be two consecutive games on four days rest, 50% of the total for this season up to then.

After that the most games that Tanaka could start would be two and he would out of sync to pitch in a tiebreaker game Oct. 5. or in the AC wild card game Tuesday Oct. 6.  The Yankees are especially vulnerable because right now Tanaka is by far their best starting pitcher.  It's not clear what the Yankees are gaining by having Tanaka pitch on "short" rest against the Mets and Blue Jays.

Aside from that, the loser of such a tiebreaker game would need to play the wild card the next day.  Then if that team won the wild card game, play first round games Thursday, Friday and Sunday: Oct. 8,9,11.  Here's the link for that schedule:

http://mlb.mlb.com/mlb/schedule/ps.jsp

If Toronto has David Price set to start the tiebreaker game against a Yankee starter other than Tanaka, the Yankees might be better off dumping that game and having Tanaka rested for the wild card game.  This could get ugly.