Yes. Realize that the power in a passage of music is split between octaves. You can hear between 20hz and 20,000hz. Each doubling of frequency is an octave so there are 11.5 octaves so in music (20,40,80,160,320,640,etc,etc) In the first 5 octaves, so approx half the scale you have 1/2 the power that exists in most music. So if you had a speaker that played 0-360 and another playing 360-2000hz on most music, the crossover would split power approx 50/50.. No realize most tweets cross around 3000hz. 3000hz -20,000hz is only 2.5 octaves, so around 15% of the power. So if your amp is set to play a song with 100 watts of power, only around 15 watts will need to go to the tweeter. Tweeters, truth be told are always weaker in powerhandling than speakers.
Generally when they rate them they rate what "program power" they can handle, so how much power is in the song, not in the part it plays, that's why you see 100 watt rated tweeters, a real 100 watts would pop them in an instant, but they don't need that much thankfully. If your just blowing your tweeters, odds are your clipping the amplifier, I'll explain why that happens next!
Clipping, has NOTHING to do with square waves or DC current or cones not moving or any other silly thing you MAY have heard, even on here lol. Clipping in a nutshell is when the amp tries to put out more power than it can, which produces both more power at the quieter points where the track could have been louder and higher order distortion at the points that were already maxed. The points that became louder are of no concern to the tweeter, as we already saw, most of it is filtered anyway. The issue is the "higher order distortion". Higher order means, higher octave. So if you distort a 300hz tone, part of that distortion is 600hz if it's second order distortion, the third order is 1200hz, etc. All this extra distortion is extra high frequency power that wasn't in the original track, so when your tweet tries to reproduce that, it's getting a real 30 watts of power now, 15 watts from the real track and 15 watts from all the extra crap the amp is adding to it! That fries a tweet rather quickly..
Since you are having problems hearing this distortion (some people don't notice it until they learn more and listen), you probably want to set yrou gains with a DMM for your components. There is a guide to that on this site in the amp section I do believe. I'd suggest a -3db tone and shoot for the RMS of your components or the rms of your amp, whichever is lower.