In general, it is important to consider future impact of decisions made on the spur of the moment. One's work history has to be represented accurately on employment forms and in interviews.
There are legal provisions for immediate termination in case of false statements at any point in the interview/application process. In this case, you may decide to gamble if you think the employer does not do background/job history check.
Otherwise, the discrepancy between what the check will reveal and your interview statement, if it was recorded in your employment file, come back to haunt you.
If you are young (<20) and want to get things straight from now and into the future, then now might be a good time to come clean. At this point you don't have much to loose. So, you need to decide how important it is for you to have the record straight in your new job, or if you want to gamble and wait until your next job to honestly disclose all your past jobs.
If the new job is not too special and you have other options, then you might just bite the bullet and tell the truth, and see what happens. They can either keep you or reject you, but at least you will be able to sleep well.
If on the other hand you worked hard to get this position and it is extremely critical for you to grab onto this job at all costs, it might be prudent to stick to your story and only disclose the truth if it becomes revealed during background check and you are directly questioned about it. (If this happens, just tell the truth: "I stupidly said I didn't have a job, but I don't really know why I said it, it was a mistake and I should have said the truth. I have learned my lesson and it won't happen again.")
Clarification: There is a difference between a resume and an employment application. It is OK to omit jobs on the resume, since that document can (and should) be revised to tailor your experience to each particular job you are applying for, 'put your best foot forward' and show only the most relevant experience (as opposed to all experience/jobs you have). The resume is your document, and you control what goes on it. In contrast, the employment application that you might get from the employer is the employer's document, and all questions on that application must be answered in the most factually accurate way possible.
Hope this helps. Good luck!