Problem redirecting output of find to a file

The first thing I would do is use single quotes (some shells will expand the wildcards, though I don't think bash does, at least by default), and the first argument to find is a directory, not a list of files:

find ~ -name '*.txt' -print > list_of_txt_files.list

Beyond that, it may just be taking a long time, though I can't imagine anyone having that many text files (you say you have a lot but it would have to be pretty massive to slow down find). Try it first without the redirection and see what it outputs:

find ~ -name '*.txt' -print

You can redirect output to a file and console together by using tee.

find ~ -name '*.txt' -print | tee result.log

This will redirect output to console and to a file and hence you don't have to guess whether if command is actually executing.