Marshall's idea is sound. On Unix-ish systems (or with a unix-ish shell on Windows), the whole task is:

sort -t$'\t' -k 2,2 file1 >file1a
sort -t$'\t' file2 >file2a
join -t$'\t' -1 2 file1a file2a >file3
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At least in Bash, $'\t' gives a tab. I'm not sure about other shells. You can always use a literal tab in quotes. The output will have the join field first, followed by the first field of file1, then all the fields (except the first) of file2. It will be sorted (lexically) by the join field. This will handle any size file as long as you have enough disk space.