The problem with your query is that you're taking the entire row and trying to insert it into the same table, along with the primary key. What you need to do is to select all the other columns except the primary key and then insert into the table, allowing sql to autoincrement the id like so:
insert into user_table (c1, c2, ...)
select c1, c2, ...
from user_table
where user_id = 1
c1, c2,... are the columns other than your primary key (user_id)
P.S. Sorry for the late reply. Weekends are for partying! ;)