Hi Trisha,
I'm not sure you're going to love this answer as it only raises more questions!
It really depends...
Firstly, if the page is especially strong (i.e. it has highly relevant links pointing to it, the site structure is strong, etc compared to your competitors), then there is no reason for your site not to rank prominently.
If, on the other hand you are competing in a tough online market and don't rank at all, then one primary / short-tail keyword / phrase is the way to go in my opinion. But this does not mean to say that you can't rank for long-tail (less competitive, lower search volume) terms too.
It also depends on how closely (semantically) related the keywords / phrases are. e.g. blue cows and blue farm animals are fairly closely related so you could potentially rank for them.
Another point is how far away from ranking on the first page are you? if you are a long way off, then you could make your name by strictly working your way through a long list of niche, long-tail terms, which, don't forget, are typically more converting too.
Make sure you put the time to check-out the competition - see how competitive the SERPs are, why they're ranking (on and off-site factors) and go from there. That should help to inform your decision.
As you can tell, it's beginning to open up a can of worms and without knowing your site and the industry it's in, it would be difficult to say exactly what would be the best approach...but work done now will ensure you know your efforts are being focused in the right direction at least.
I hope that helps, just a little....
Ben
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