I have an idea for a business - a service that solves a particular pain point for a well-characterized market. The thing is that this market is not large - I would say at most a million US citizens, at least 150,000, plus perhaps a hundred thousand more worldwide. This market is currently served by a brand that is horrendous, but which is a solidly established market leader due to network effects and a freemium business model. By offering a better service, with backwards compatibility (Spolsky 100% sold me on this point), I plan to disrupt and replace the current market leader. In addition to the matter of size, this is not a market with a potential for explosive growth - if I get it right, it'll have perhaps a year or two of fast growth, but will plateau into growth at single-digit percentage rates after it's soaked up market share from the current market leader. As well, this idea requires more lawyering up than the average "here is a website through which we provide a service" startup, because of concerns with user-generated content and the normal way that a startup that makes money becomes an appealing lawsuit target (this one more so than most). On the bright side, apart from retaining counsel, the business costs are perfect for the lean startup model; create the software, scale it up with EC2 and other on-demand cloud computing/storage services as needed. It's not like it's unusual, either, for a startup to live in a position of "if we get sniped by a lawsuit, we go out of business."
That's the background for my question - am I targeting a big enough market to seriously pitch this idea to angel investors? It's a tempting thought, because $100,000 would buy me two years of runway as a solo founder, three years if I did a good job of running lean - but because of the business model I'm targeting, I probably can't offer investors the classic startup upside of "if we win, you get a 20x or more payout." This is not a business idea that's headed for a big acquisition or an IPO - the reason that I'm not telling you the specific business idea, in fact, is not because I have a Winklevossian fear of my idea being stolen, but because the idea sounds like a joke, especially in the context of an IPO or a high-octane acquisition. Should I go for bootstrapping and/or friends-and-family funding? The tradeoff there is that at that level, I can't quit my job to work on this idea, and on the nights-weekends schedule, I estimate it'd take 2+ years to get the product developed, marketed, launched, and ramen-profitable. I'm a hacker: I'm greedy and impatient, and I want to be able to quit my job and work on my great idea, dammit! But I've created enough hacks in my time: I know that the ideal way to do it, sure as heck isn't the only way to do it.
Which, in turn leads to another way to phrase the question: is this a proper startup, or is this a lifestyle business?
To answer your specific question: you have a lifestyle business. At $100k, you are in the friends and family range, not angel range. F&F can fund a lifestyle business. Angels won't fund a lifestyle business.
To give you some critical feedback...
$100k will not give you a 2 year runway. That's a 10-14 month runway. I don't care if you live with mom and dad, eat top ramen for every meal and don't shower to save on your electric bill...you can't make $100k last 2 years. And if there is ANY chance of a lawsuit, forget it.
You described your competition as 'a solidly established market leader'. Have you ever built a business that took market share from the single incumbent? If not, you have no chance in hell of success. If you have done it before, then you might have a chance. Of course they are a 'horrendous' company with a crappy UX, crappy customer service, etc. However, you're assumption that 'offering better service' is enough to take market share is simply unrealistic.
If it takes you 2+ years to get to ramen-profitability, this is absolutely a waste of your time. The risk-versus-reward is simply absurd.
There are SO MANY opportunities for a hacker out there, that you really shouldn't waste your time on this opportunity. I realize this is the best idea you have right now, but don't bite on it.
Keep looking for a better opportunity. You really don't have to look that hard to find a much more reasonable (i.e. lower risk, higher chance of success and bigger upside) than this.