Exactly what I came to post.
It depends on a variety of factors, but most notably -- what you enjoy working on. 10+ years ago, I hated working with Javascript (and it wasn't nearly as pervasive), so I refused to learn it, which meant that I didn't have to do any work in it for any prolonged period of time.
On the flip side, Javascript has really turned itself around now, and I feel somewhat disadvantaged now (though working towards greater proficiency.)
If you want to be a front-end developer, you needn't really have more than a cursory understanding of how a backend works, what variables you get out of it, and what you expect to put into it. You should know how template rendering works, and beyond that, you're kind of exempted from the rest.
Many of the best designer / front-end engineers I've worked with were fairly ignorant of what happened on the server side, but that didn't stop them from kicking insane amounts of ass.
There's a trade-off, generally. I consider myself a 'full-stack' web developer, which means that I can build every aspect of a web site from the database (or NoSQL db) to application layer to the presentation layer to marketing to SEO. It won't be as pretty as if a designer had been involved, but it won't be disgusting either -- but that means that when there are jobs for front-end engineer, I am again disadvantaged because I don't quite have the depth of knowledge required for a more focused position.
My core competency is in Python, but often, when I get around people who focus on Python exclusively, I feel behind the times compared to them because I am 'wasting' time making sure I follow updates to CSS, HTML5, Javascript, etc.
I don't hate any of this, mind you, but the "mile-wide, inch-deep" category opens a lot of doors while simultaneously closing others. Same thing with the "inch-wide, mile-deep" type of learning that specialization will get you -- you are now very qualified for a particular kind of work, and less qualified for other types.
In practice, we all know that someone competent in one area can generally adapt, so the limitation is really only so damning as your ability to convince somebody that you could 'pick it up' regarding a new topic, but it's whether or not you want to. At least for now, it's a buyer's market in the job force, so you should have plenty of opportunity to entertain offers and pick from those that suit you best, so there's not really a wrong answer. Whether or not that will change the future I can't say.