An American friend of mine living in the Philippines with nothing much to do landed a gig for $100 to build a landing page using a WYSIWYG HTML editor. He had only ever built a few sites using this editor and knew next to nothing otherwise. I think he was even able to complete it within a few hours. So, yes, as long as you are willing to spend time to do something for somebody else who doesn't have that time, then you can get paid.
If you are looking for an actual full time job, then this is highly unlikely.
Web development shops don't do training. They are looking for people who can hit the ground running with little or no help. Making a web development shop work is difficult, and someone with little experience will only cost the shop money, which creates a burden for the business. They also need people who are well rounded, so that one person can do most of what they require, what's left over can be outsourced.
Startups are much the same as web development shops. They don't have the resources to train people and they need for their developers to be well rounded.
As a JS developer you would be a specialist, and specialists can really only get freelance work from development teams who don't have enough free resources in that area to finish that part of a project but don't have enough work in that area to justify hiring someone full time.
Large established businesses which have a lot of resources (or startups which are very well funded) are in a better position to train people. They may also be more open to doing so if they have to quickly ramp up their development staff. But you probably won't get into a Facebook or a Google without excellent credentials (graduating from a big name school if you don't already have experience) and getting through a daunting interview process.
There are exceptions out there. See hungryacademy.com (for LivingSocial) as an example, but this is not the norm.
The easiest way to land work right away is to go the freelance route. Unfortunately, this can also be the most difficult route to make a living as you would be running a business and managing cashflow as opposed to receiving a regular paycheck. With an employer, you can get paid through your learning curve, but with freelancing your learning curve may result in being late on rent (and figuring out how to make freelancing really work can take years for some people.) This is also a bit of a backwards route because ideally you would first become an expert by learning from a successful web development shop before striking out on your own.
However, at the end of the day, we are all hustling. We need to somehow get from point A to point B and by sheer willpower we will figure it out (or get replaced by someone who will.) You need to also be hustling and eventually you also will find a way.
My suggestion.
The next logical step from JS is to make sure that you are functional in HTML/CSS, as that gives you a solid foundation for front-end web development work. At this point, you would still be a specialist, so you would need to go further. The HTML/CSS is often done by designers or can easily be outsourced because there are a lot of solid people in this area. So this alone won't land you a job unless you are a solid designer. Again, the details vary depending on the employer.
Because you have mentioned objective-c, I'm assuming that you are not a designer and would need to go the coder route. So, you will need to augment your front-end skills with some back-end skills. As a coder, you don't need to be a wizard with HTML/CSS because of the already mentioned reasons. Just be good enough that you can put together those elements if you need to. You now need to select a general direction for the back-end. PHP, Ruby or Python are the most likely choices here.
You need to consider potential markets before making a decision on your first back-end platform. The market for PHP developers is huge, but there is also a ton of competion. The market for Clojure developers is relatively small, but you also have less competition. Additionally, you could further drill down into specializing on specific content management systems, such as Wordpress, or frameworks, such as Rails. Take a look through available jobs (as well as the budgets and the competition for these jobs) at Elance and Odesk to get a feel for this.
Once you have started to learn your chosen platform, you need practice every day until you find that you are able to take care of the basics without having to look through documentation at every step of the way. At this point you are functional and you need to start publishing some code to Github as potential clients or employers will ask to see samples of what you have done.
Your next task is to come up with a project where you take care of everything from A to Z. If you have followed the above advice, then this is probably a web application. Make sure that you finish the application and get it shipped. Do some light promotion to get a little traffic. This will give you an idea of what the entire process of creating a web application requires and will help fill in some of the gaps that the above advice didn't cover.
Congrats, you are now functional enough that you can start considering your options for building an income. You now need to start networking (actually, start this process as early as you can.) Find the communities for your chosen platforms / markets and start participating. In particular, look for places where paying clients are part of the community.
Notice that I haven't touched on Objective-C. You could probably take the same route with Objective-C but I don't have the same experience to make suggestions in that area. Javascript is a scripting language for web applications, so I would suggest that since you put in that time that you continue following the web side of development. Go through my suggestions and then make the decision of continuing with web development or making the move to native mobile apps. Personally, I wouldn't want to get started with mobile apps without having web development experience under my belt.