How can I run a SQL job every 1 second?
Create a job that is scheduled to start every minute. Have the job do something like:

WHILE 1=1
BEGIN
    EXEC dbo.SomeProcedure; /*  this would be the 
        name of a stored procedure that does the 
        actual work */
    WAITFOR DELAY '00:00:01.000';
END


Thanks to Max Vernon, who gave me this answer earlier.