The impact it could have depends on several factors. One of them is how much work a potential employer puts into checking out your work history. If you don't include a job on your resume, they aren't going to know you worked there, which means they won't know the circumstances of your leaving. So the very short term job you were at for just a few weeks I would say don't even include on your resume. Most employers will not provide details of how/why you left a job, they will simply say you are eligible or not eligible for rehire.
Seasonal jobs are hiring right now, which could get you employment for the next couple of months, but in January you could find yourself in the same position. If you are looking for a job to work while you go to college, you might want to check with your college to see about jobs on campus. There are often positions available in different areas, and they are usually pretty flexible about working around your schedule. The only problem is that you need to find something else to do during break and summer, because those positions aren't generally used when class isn't in session. But if you do a good job there you can usually come back year after year, which is also good. I worked through college, during school I worked on campus for the university, and in the summer I worked for the library in my hometown. Not glamorous jobs, but they paid the bills.