Does my amp have enough juice to power my speakers?

There is no such thing as a speaker needing power. Speakers don't need any power at all. Listeners do. Its you that needs the power, and the louder you like your music the more power you need. Regardless of the speaker, or its sensitivity, or any of that.

Regarding power, the one question you need to really ask yourself is: If the first watt isn't any good, why would you want 200 more of them?

84dB sensitivity needs power.

To do some math:

Placing it in-room would lead to about a 2dB boost (3dB for speakers with deeper bass), making it 86dB. If you sit 12ft away, that’s about a 7dB loss, so now it’s 79dB. If you wanted peaks of 100dB, you would need ~125W.

If you sit 6ft away and wanted peaks of 100dB, you would need ~65W.

Do they sound heavenly and eeeh playing the same music?  If so, then it's definitely something else.  If you can find a correlation (demanding source material) then it's probably the amp.

The sensitivity of the speakers is what counts relative to needed power...my 12wpc single ended tube amp through my 99db efficiency speakers will knock yer tattoos off. 

eric has a good point on power quality IF your sound quality varies nite by hite but the SPL and music you are listening to remains constant.

my reference system is bi-amped at 1.2 KW per side, w speakers in the 84 Db class for efficiency, but I never use that ( how do I know ? DMM, SPL meter and an RTA....good tools are cheap, your hearing is not )

I have two other 40 WPC systems that provide adequate SPL for peaks w 86 db class speakers in rooms to 15’ x 35’, of course I dont listen all that loud...certainly no 100 db peaks....

on to your amp, audiogon member contemplating purchase of the 86 db speaker hauled his amp over to my place for 4 hour listening session at levels louder than I normally push - amp held together pretty well and dialed back just a smidge was liquid velvet, its certainly a musical amp. It was running off Isotech power conditioning....

finally for those who dig the high SPL world, get hearing tested....