Undergrad thesis supervisor rejected request for LOR - how will this look on grad apps? I haven't worked with my supervisor for long (~3 months now, 4 when apps are due), and she is well known in her field. I understand she has a reputation to uphold is honest in her letters from what I hear, so she really needs to get to know you before something like this. 

I will be giving a lab talk on Nov 15 and submitting a research proposal and lit review on Nov 19, but sadly apps are due earliest by Dec 1. So, again, understandably, she told me she didn't feel prepared to judge me in a span of about 10 days (between when I submit and when apps are due), and that I should seek another prof. 

Luckily, I'm working on another independent project and I've asked that supervisor (fingers crossed!); my other references are from (1) a 1.5-year work supervisor from when I was a research assistant and (2) a prof I worked with for a summer independent project. 

How will it reflect on my Master's applications if I don't have a reference from my thesis supervisor? Is there anywhere I can explain the situation? Or, is there a possibility to request a delay in submission anywhere - and if this is the case, should I mention it to my prof or should I not persist?
It's generally a good idea to have at least one reference from a research supervisor. It's sounds like you have one, possibly two, such references, so that is no issue. Given that you've only worked with your current supervisor for a few months (and haven't even submitted your proposal yet), I don't think the lack of a letter from her will be suspicious. 

In terms of the options you list:


As far as I know, getting extensions on grad school apps is not really done. 
You could wait until the next cycle, but that seems extreme. 
Rather, I would just proceed with your application as-is, clearly indicating that your primary research mentor was [the person who wrote your letter] and that you only recently started working with [the person who didn't].