Well, let me ask you this. Normally I'd call in a day or so to follow up on a resume submittal if it's a job I'm super enthusiastic on. This one I am particularly interested in. It just so happens that they happen to be damn near within walking distance of where I live. I know that people aren't supposed to blindly walk in to businesses and drop off unsolicited resumes. Do you think it'd be a good impression to walk in to follow up and drop off a physical resume?
I wouldn't want to recommend anything in particular. Employers are all different. But if you decide to walk in, you could say: 1) I was wondering if you received the resume I sent a couple of days ago. Could you check? 2) Do you know when HR will be making a decision? 3) I might be leaving town over the holidays and I would really like to find out more about the job before I leave. Can I meet HR briefly now? 4) I sent in my resume by email as the ad suggested, but I'd also like to drop off this letter of recommendation. It's stapled to the back of this hard copy of my resume. 5) Please give HR this xmas card and bribe. (ummm, just kidding).