Is there a maximum length constraint for a postgres query?
For current PostgreSQL version (up to 9.5), queries are received by a backend in a Stringinfo buffer, which is limited to MaxAllocSize, defined as:

#define MaxAllocSize   ((Size) 0x3fffffff) /* 1 gigabyte - 1 */


(see http://doxygen.postgresql.org/memutils_8h.html)

So a query is limited to 1 gigabyte (2^30) in size, minus 1 byte for a terminating null byte.

Should a client try to send a larger query, an error looking like this would come back:


  ERROR:  out of memory
  DETAIL:  Cannot enlarge string buffer containing 0 bytes by N more bytes.


where N is the size of the query.

Be aware that a query just below 1GB might require large amounts of memory to be parsed, planned or executed, in addition to that 1GB buffer.

If you need to push a large series of literals into a query, consider the alternative of creating a temporary table, COPY rows into it and have the main query refer to that temporary table.