Assuming you're looking for username and id columns, then that's not proper SQL syntax.
The main issues are that you're column names are enclosed in single quotes and in parentheses in your select. Try changing it to this:
SqlStr = "INSERT INTO UserTimeStamp (username, id) SELECT username, id FROM Staff WHERE password = '" & passwordTB.Text & "'"
That will get sent off to SQL like this:
INSERT INTO UserTimeStamp (username, id)
SELECT username, id
FROM Staff
WHERE password = 'some password'