To get back to Tigger's problem, it sounds to me as though, before you do anything, you want to get looking at your logs. Just seeing where you are in the search engines doesn't tell you whether anyone is coming to the site through those searches.
It could even be that people are arriving from search terms that you haven't considered. (In that case that is a pointer for more content - perhaps a separate page targetting that term.) Also look to see if people are hanging around, or are they taking a look at the home page and disappearing. If they are, it could be like you say that the home page is actually putting off people, and that gives you ammunition to proceed.
However, do be aware that it could also be that people searching on that term are not likely customers for you. That happened to me once - lots of people were arriving (it was a technical term that I hadn't consciously optimised for) and immediately leaving. When I went to look in the search engines, I was surprised to see that there were no companies that I would consider to be competitors of this site anywhere in sight on the page. The reason of course was because people looking for this term were actually wanting something quite different.
So what I would do is look at the logs. Find terms that people are sticking around for - they are obviously happy that they have found a site that helps them, so those terms are good for you. But also look at terms where people are moving on sharply. If they are what you consider good keywords, and you have checked that your competitors are all over those terms, then that is a big potential market that you can go for.
Your home page does not need to be only targetting a couple of key words either. Remember - it works very well if the home page is a call to action to all the services you provide. Skilfully done, it can sum up all sorts of stuff on your site and point people to where they should be going next - calls to action - and target loads of good keywords to boot. Perfect for your visitors and not bad for the Search Engines too!
Jo