Find the closest palindromic number

Pyth, 26 20

Lnb_bWP`+QZ=Z-g0ZZ)Z

Updated to meet the new rules.

The program runs in an infinite loop which tests every possible increment, in the order 0, -1, 1, -2, -2 ...

Explanation:

Q=eval(input())     implicit
Z=0                 implicit
Lnb_b               def P(b): return b != rev(b)
WP`+QZ              while P(repr(Q+Z)):
=Z-g0ZZ             Z=(0>=Z)-Z
)                   <end while>
Z                   print(Z)

Example run:

python3 pyth.py programs/palin.pyth <<< 965376457643450
-2969881

This took 23 seconds.

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Bonus solution, same character count:

Wn`+QZ_`+QZ=Z-g0ZZ)Z

Ruby, 111 84 bytes

i=$*[j=-1].to_i
r=->j{s=(i+j).to_s
abort(j.to_s)if s==s.reverse}
loop{r[j+=1]
r[-j]}

Takes the number as its only command-line argument.

CJam, 34 29 25 bytes

q~:I!{:R1<R-RI+`_W%=!}g;R

Try it online.

Examples

$ cjam palfind.cjam <<< 120; echo
1
$ cjam palfind.cjam <<< 121; echo
0
$ cjam palfind.cjam <<< 122; echo
-1

How it works

q~:I    " Read from STDIN, evaluate and save the result in “I”.                           ";
!       " Compute the logical NOT (0 since the integer is positive).                      ";
{       "                                                                                 ";
  :R    " Save the topmost integer in “R”.                                                ";
  1<R-  " Compute (R < 1) - R. This produces the sequence 0 → 1 → -1 → 2 → -2 → … .       ";
  RI+   " Push I + R.                                                                     ";
  `_    " Cast to string and push a copy.                                                 ";
  W%=!  " Check if the reversed copy matches the original.                                ";
}g      " If it doesn't, repeat the loop.                                                 ";
;R      " Discard the integer on the stack and push “R”.                                  ";