Here's the opinion of someone who majored in math (at a top school in the United States), but was not a genius at it.
This is a condensed, generalized, down-and-dirty opinion, but I stand by it.
Your assumption about being well-covered is more accurate that not. If your intent is to form a mathematical basis of strength that you can apply to applications of math (e.g. finance stat econ) then undergrad is as far as you need to go with it. By the time you take Real Analysis & Complex analysis your mind will have developed in an amazing way. As Matt Pressland said, you learn how to learn Mathematics. Matt also mention the difference between that style of meta-cognition and being able to research. It's impossible to say today that you could or couldn't come up with a unique research idea that would be considered a contribution and that you're passionate about to pursue. However, unless the word research makes your heart throb, you don't need Math graduate school.
I've rewritten the rest of my answer to be a bit more compact.
Do not major in math, minor in it. You will gain a superior analytic mind. However, your employment potential depends on not being a Math major. The Corporate world (Actuarial aside) doesn't know wtf Math is. They will ask if you wanted to Teach High School.
Accounting is boring, and Economics is fluffy. Choose Statistics and augment with Finance. Also, Computer Science requires more hours spent at 1-sitting than Mathematics. Engineering trumps Computer Science as you can learn to be a programmer in your spare time.
First know what you want to do as a career. Do not decide this on your own. Go to your career center for expert help, and shadow professionals and intern. Funny how this is #3.
Math can be a minor. Let your possible career path determine your major. At the least you can be earning a salary when you're 22-23 while deciding what new career you want. At the best, you'll save yourself 3-5 years of searching, finding-professional-self, and rebuilding qualifications.
I decided to add some external links that would shed light on why some of my views are as they are. These come fro the Bureau of Labor Statistics... Oh look Statistics is even in the name =)
A small summary is included with the link, but please click and compare.
These are just samples, you can find your own BLS data to refute if you want.
Occupations from mostly-pure discipline
1. Economist. $43/hr. 6% projected growth. 15.4K jobs. Bachelors Entry-level
2. Mathematician. $48/hr. 16% projected growth. 3.1K jobs. Masters Entry-level
3. Statistician. $35/hr. 14% projected growth. 21.5K jobs. Masters Entry-level
Occupations heavy in STAT with Finance Augment
4. Financial Analyst. $35/hr. 26% projected growth. 236.0K jobs. Bachelors Entry-level
5. Actuary. $42/hr. 27% projected growth. 21.7k jobs. Bachelors Entry-level
Conclusion for the sample
Stat has way more job positions filled/needed much faster growth than Econ, same entry-level as Math.
Finance augmented, Statistically heavy jobs are quite abundant, pay well, and grow fast. This is what I recommended. I recommended majoring in Stat with a Finance augment. Both examples of this require only a bachelors and are in a job space projected to grow much more than the Mathematician or the Economist. The pure Statistician indeed makes less than those two. So to repeat from previously: Math Masters not needed if you like other things. Don't major in Math in undergrad.