Delaware: Taylor--6,440 / Cass--5,910. Votes needed to chage: 266
Georgia: Taylor--47,532 / Cass--44,785. Votes needed to chage: 1,374
Louisiana: Taylor--18,487 / Cass--15,379. Votes needed to chage: 1,555
Total votes needed to change: 3,195
Electoral Votes: Delaware--3, Georgia--10, Louisiana--6.
Electoral votes needed to win: 146
OTL's EV: Taylor--163 / Cass--127.
163 - 19 = 144 / 127 + 19 = 146
That is the easiest way to make Cass president and involves the smallest number of voters needed to change their mind, and less than 3,200 people isn't too bad.
It also deserves mention that most believed that the Democrats had the election in the bag, a big reason that Taylor vacillated between parties. That the Whigs nominated Taylor was actually a sign of how desperate they were to win the presidency. It really was an "Eisenhower '52" situation, but if Ike had chosen the Dems and beaten the GOP.