The longer you can stick it out, the better off you will be when you look for a new job because you will have a reference and some work history. It does sound really crap and I don't blame you for feeling down, but I would not leave without some other job to go to if I were you - stick it out as long as you can get out of it, get some money and, more importantly, get some work history behind you.
If there are people that are being more successful than you are at getting the surveys filled out, ask if you can listen in to what they are doing for 30 minutes to improve - maybe they just are saying things differently than you are and you need to try a different tract or tone to engage them. It's hard when you're starting out at a new job, so learn from some people with experience doing what it is they need you to do.
Stress and anxiety are totally 100% normal in a new job - everyone feels that way and it will be that way in any new job. Wanting to make a good impression and not really knowing how things work lead to that feeling. It is totally normal and would be the case in any job. If you are not performing well enough it is okay to ask for guidance on how to improve - shows you are serious about the job and want to do well. Please don't quit before you've got some use out of the position, even just as work history/something on your resume that won't lead to "why did you only manage such a short time?" questions.