Given my working assumption that every human tendency is on a spectrum, it seems reasonable that love, too, is on a spectrum. But this is controversial, because it implies that there are degrees to how much one loves, whereas in popular conception there are no degrees to love, the question is a binary "do you love me?", and that's that.
So, is love an exception to the no thresholds assumption? I'm thinking no, and here's why.
First, I agree with Elie Wiesel, who said that "the opposite of love is not hate, the opposite of love is indifference." This makes sense because hate is often correlated with love. Think of Elizabeth and Darcy in Pride and Prejudice.
Second, love is usually a relative term. Competition of one particular love over other possible loves is implicit. To tell someone that you love them, but that you love everyone else just as much, is basically to say that you don't really love them.
Given the above, this is my preferred model. We have a spectrum of how much we care about a given thing. This spectrum runs the gamut from totally indifferent to really, really caring a lot. You can always care more, you can always care less. "Love" is the state of being at some point among the set of caring levels above some arbitrary point, the "love threshold." This diagram may help you to visualize:
Nevertheless, where one defines the love threshold can vary based on, among other things, jadedness, neediness, and drunkenness. This variability underscores that the concept of love will always and forever be an abstraction, a human construct designed to serve our far mode ends.
Edit: See Lemmus's insightful comments below, suggesting that I change "caring" above to "liking," which makes sense and is more consistent with the difference between love and hate.