No, no, no. Do not do this. It is bad advice!
First, asking for ANY precommitment not to break up over X is going to be a "major relationship step" and unless you are very experienced with relationships it is not something you ask for during the first two weeks, because there's a decent chance it'll harm or end the relationship.
Second, it's a stupid precommitment to agree to! There's all SORTS of good reasons to break up with someone who texts you, since the content can be basically anything.
Third, any breakup can be blamed on texts / emails, so it's a big red flag that you're going to be a serious creep if you ever do break up with them.
Phrased more specifically, in a stable, long-term relationship, and done by someone who is fairly experienced negotiating boundaries, this CAN be useful, but none of those qualifiers seem to apply here!
I wasn't saying to commit to not breaking over the content of a text message, but to commit to not breaking up over the medium of texting.
Even in a two week old relationship, I think it's reasonable to say something like, "Hey, I enjoy hanging out with you, and it seems you feel the same. If you change your mind though, please don't tell me over text or e-mail, just give me a call."
I started going out with a fantastic girl a couple of weeks ago. Everything is great, except that whenever I've sent her a text message or email requesting something and haven't received a response yet, I experience significant dysphoric anxiety, fearing that her response will be not just "no" but "no and I don't want to date you any more". This is due to brain chemistry or personal history, take your pick—either seems like a possible explanation to me. But there's certainly no evidence supporting the idea that this is likely to happen, nor is the anxiety helping me prevent it or helping me in any other way.
Does anyone have evidence-based advice, or pointers to same, on dealing with this kind of issue? It is the only splotch on what have otherwise been the best two weeks of my life.