for most companies is hugely in favor of the programmers. A few years ago I needed to hire a college-grad CS major for (non-web) software development. I contacted the local university and received several dozen resumes, and nearly every prospect was highlighting their web design experience and looking for a job doing the same. The exception to that were the foreign graduate students, whom I could not hire for security clearance reasons, and one previously home-schooled kid (for high-school) that fast-tracked his way through college and was not stuck in that web design rut like everyone else. While I found two other candidates I could barely justify interviewing (because of what they did for hobby programming, not what they espoused in their schoolwork), the previously home-schooled kid got the job. No contest, really. I was mad at the school for producing so many no-interview/no-hires and wrote them a letter saying as much.
The company I worked for at the time employed 90-100 people, with about 25 of those being software developers. We only had one web designer and he was also doing all the IT in three cities, so web design was very part-time activity. The most important part of our web-presence was CRM software, which we wisely outsourced to a big-name company which hosted that portion for us. We paid that company about half of what we'd pay one full-time programmer and it handled thousands of customers. That left our IT/web designer doing fairly rudimentary web development.
It is a scaling issue. The tiniest company that needs a rudimentary web presence might do web development in-house with a poorly qualified individual and then later maybe outsource to gain a fairly robust but static online web presence. Once they are big enough to hire a competent in-house web person, they still won't need to hire a second web developer until that company is either very large, or doing something very unusually interesting online--and outsourcing can usually be done cheaper in most of those cases.
The bottom line is that you should concentrate on school and the non-web oriented CS courses that school can offer you. Most companies don't need anything fancy or unusual for web design and a university that is pushing more than one class in that area as part of a CS degree is exploiting the students' ignorance of the job market. There is more than enough fundamental things to be learned in CS without getting bogged down in teaching whatever the latest trendy web tools are.
If you need to earn money, offer your part-time services as a consultant to small mom-and-pop businesses that have crappy websites. As a demo, repackage what they have into something less crappy. Send them a link and then offer to revamp and maintain their website. Smaller churches are another good candidate and could probably use a part-time IT person to help them from time-to-time. Line up a few of those each year and you'll have a nice side-business and resume to augment your degree.