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I would say that it is a promising field. Even with the prominence of the iOS or Android apps, web development is still the most demanded framework to use in the enterprise field.
In order to secure an internship (there are millions of them in that field) get some practical experience that you can show in a resume... do your own community or personal projects, participate in some open source project, and learn multiple frameworks and languages.
Software Engineering is currently ranked as the #3 job to have in the United States by US News (http://money.usnews.com/careers/best-jobs/rankings/the-100-best-jobs) and is consistently considered to be one of the best jobs for new graduates in America. All that to simply say, Web Development is a wonderful focus to have in college.
I would recommend you contribute to an open-source project as a way to secure an internship. Take a look at: https://help.github.com/articles/where-can-i-find-open-source-projects-to-work-on/ as a starting point.
Networking is also important. Create a professional LinkedIn page and add all of your existing friends, family, teachers and people you meet on daily basis in the workforce. One of the best ways to land an internship is by by professional networking.
And finally, consider purchasing your own domain and creating a website. You can use Webstorm (free for students: https://www.jetbrains.com/student/) along with, for example, Node.js and Angular.js to showcase your abilities.
I hope this helps!