I applaud the speaker-first camp, a good debate needs camps. Sure the speakers have an enormous effect, and there is great variation between speakers. You have to find speakers you like, not speakers that are just highly-rated. Also, speaker design is a tricky art; surprisingly few makers get it right, and not necessarily with all their models. Better to find a well-designed one and never mind whether it costs a little or a lot.
The main point of having a good source has to do with upgrading.
If you plan never to upgrade any more, don't worry about your source quality. The thing is, though, that even a cheap (but well-designed) set of speakers will reveal the quality of a good source. The same speakers, and much better ones too of course, will reveal the faults of an ordinary source, and they will do it mercilessly. So if you are planning to wait out the time you take to save for an upgrade while listening to your system (and who wouldn't?), you stand a chance to have more fun if you upgrade the source first, then the speakers.
That's the point of "source first" when you're upgrading.
The other point of "source first" is simply the same one you keep in mind when you resize a digital photo. If the original has more dots per inch than the final image, you will get a nicer-looking picture than going the other way. Thus the highest-resolution component should probably be the source.
In a mature system, the difference in resolution doesn't have to be very great, though, and that's why this point is not as critical as it is when you're planning upgrades. A system that is transitional, being enjoyed in view of future major upgrades, is more likely to have an imbalance between the quality of the components. If that is the case, keep the highest quality upstream, and upgrade from source down.
Right now, your best component is of course your amp, and you could go either way as you upgrade. If you found the speakers of your dreams right now, it would be tempting to go for them. If they really were the speakers of your dreams, at the right price, you probably should. Otherwise, though, buy the best source you can now, and do the speakers next.