Avis. The car rental company.
When you’re number 2, you try harder.
ETA: And I see I am no. 2 to post this response. Guess I’d better try harder.
A 2-10-4 steam engine.
The second item on some list.
Hair gel.
poop should always be “number 2” never “No. 2”
I said the pile of poo, but I really just think of someone who needs to defecate. I’ve heard people say, “He’s going number two,” or “I need to go number 2,” but not “He left some number two in the stool.”
My first thought was a No. 2 pencil. As for shortstops, I’m a Rockies fan, so I would have said Troy Tulowitzki. 
I thought of Robert Wagner in the Austin Powers movies.
There’s a New Zealand film called No.2 that I want to see, mainly because I really like the guy who did the soundtrack - Don McGlashan, ex Mutton Bird, and want to hear it in context.
Simply the second item. For a moment I’d look back a sentence or two for “No. 1” since I read very quickly by scanning blocks of text. Barring that my brain would probably jump to a pile of poo.
Precisely. With “number” spelled out I’d likely have voted “poo”, but the way you’ve written it in the OP immediately conjures an image of a Dixon Ticonderoga No. 2, complete with metallic green foil stamped lettering.
This makes me think that you are, like myself, yet another person who has taken WAY too many standardized tests. 
The ONLY thing I could think of before I read the poll options was a pencil.
Something Else: the second in a pair or series.
My first thought was; what’s number 1? So I went with the second smallest interger.
My no. 2 thought was poop.
Austin Powers
Austin Powers, specifically the sound of Dr. Evil saying “Numberrr Two”.
Needing to go to the bathroom, but I live in a civilized country - no piles of poo, that’s what the porcelain throne is for!
When I read “No. 2” as written, I think of the pencil.
When I hear “number two” spoken, I think of poo. I tried very hard to not laugh last night when Spike was the second to finish his dinner, and he very proudly announced, “I’m number two, Dad!”
This is all rather interesting, but I have to think about why 
The reason I made this poll this exact way was based on a few insights I had for no particular reason, after making a three-way pun earlier this week about a sports team often considered a perennial runner-up that got compared to “poo” by their principal owner and in a sarcastic letter, suggested they seek a sponsorship from Dixon Ticonderoga. (It was about the NY Mets, a team for which I am a season ticket holder.)
1 - That the textual phrasing “No. 2” suggested the pencil due to its being a somewhat old-fashioned abbreviation in America, due to the specific instruction to use a “No. 2 pencil” to fill in the multiple-choice bubble sheets in many standardized tests that has probably been cut-and-paste as boilerplate since the 1940s. (The pencils themselves simply have the numeral “2” on them, and the boxes sold in stores actually read “#2”.)
2 - That the phrase “number two” would be verbally associated by many people with “poo”.
3 - That the concept of “poo” is deeply wired in our pysches as a hot button. Young kids love doody humor, and adults consider scatalogical references impolite and bawdy.
4 - That people usually read things “in their heads” (as if read to them aloud).
5 - That people usually read a poll’s answers quite quickly - quickly enough to change their minds on the answer based on what they read even if the poll says “what’s the first thing you think of…”.
6 - That the word “poo” (as opposed to dung, shit, crap, feces, faeces, droppings, leavings, fewmets, patties, lawn bombs, etc.) is intrinsically silly because of its childish association.
This poll proves none of the above, of course (not enough controls), but I did carefully construct it so that the title used the phrasing “No. 2” (intended to evoke the pencil association), then put “a pile of poo” as one of the middle choices (not first or last). I used that somewhat childish phrasing too to improve the odds of it catching people’s imagination, to evoke that inner 7-year-old who giggles irrepressibly at just saying the word “poo” three times aloud. (I also considered “doodie” or the doubled up “poo-poo”, but a simple “poo” seemed more euphonious with the word “pile”.)
My theory would be that without “a pile of poo” being one of the choices, the pencil answer would be the runaway winner… But by adding it to the poll with that particular phrasing, that I’d get a lot of hits due to it sticking in people’s minds by the time they finished reading the list of answers. And that many people would admit to doing so in follow-up comments (which they did). They might feel “guilty” to change their true initial answer if “pile of poo” were the last answer, and to a lesser degree if it were the first one, but putting it in the middle should draw the highest conversion rate.
I can’t really draw that conclusion without at least two control experiments - with the “no-poo” poll as one test, and another one with the entry described more prosaically (“a quantity of feces”), and maybe more to change where in the list of options it fell - and besides which, I have no idea what such “research” would even have as a point.
But it just seemed like a fun thing to try to find out in a cursory SDMB way.
Oh, and of course the SDMB has plenty of international (non-US) folks who would probably not have the pencil association. That probably contributes to “pile of poo” ultimately overtaking the pencil answer, in addition to all those dishonest and/or juvenile poopie-heads 