Do we see protocells forming in nature today?
we don't think so, some parts are easy. liposomes form all the time, and can be created in lab quite easily. They quite readily encapsulate any material present when they form, including DNA. So once you have the right stuff (likely RNA) it is very easy to enclose it in a lipid bilayer. 

RNA has been formed from scratch in a lab it is even easier than we thought it would be. It may form in nature today but is unlikely , the current atmosphere is very oxygen rich and bacteria are not just willing to eat RNA but also basically all the chemical building blocks as well so it is difficult to build up a concentration of the precursors in nature today. 

Worse evidence of it forming today would be ridiculously difficult to demonstrate because there is a constant contamination of biologically produced RNA from decaying organisms. There is basically no place on earth today with liquid water that does not have life in it. 

Here and here is a review of our current models for the origin of life, Be warned the first link is a file.There are many steps involved to get a cell but it all starts with the first molecule capable of making copies of itself.

Forming self catalysis strands in a lab would be the best evidence but has one major problems, Money. Earth had an ocean sized laboratory and millions of years to stumble one of the strands with one of the right codes through random chance (remember a self-replicating code only has to happen once) which likely could only be duplicated by doing millions or even billions of identical laboratory experiments.

Finally while the Urey-miller experiment was historically important it is by no means the best nor most modern experiment you can find much more information about the variety of experiments at this question.