As a current student at a college with a strong engineering department, I can tell you that those who do drop engineering generally do so because it's too hard, and instead generally go into teaching or some lower-paid field. Engineers (along with accountants) generally have the best career prospects of those who stay with an undergraduate degree.
In this economy you want to be a specialist in something that people will pay for. If someone gets a general business degree or some liberal arts degree, they might as well take the LSAT now, cuz I know that is where they will end up. If you can help a company build their IP, you are in a good spot. Engineering is a great place to be in that respect.
when a company like Cisco - dominant in their particular space, tells you they plan to hire more engineers in India then in the US - don't put too much stock in what you might think your "job prospects" are. sure, there are jobs - but fewer and fewer careers. more contract work means people are employed for 9 months out of the year, and looking for their next assignment for 3 months (unpaid). and trust me, the mid and upper level managers are actively working every day to figure out a way to get job functions moved offshore.
I judge it based on my colleagues at work, what they are doing with their own college bound kids - I cannot think of a single one, who are sending their own college bound kids to "follow in their parent's footsteps".
my advice to you - complete your undergrad engineering program, and go get an MBA in finance or business or marketing. that combination does very well, as US corporations will not offshore their management cores. you can earn good money with that combination.