Question about Nimble Obstructionist and Thrashing Brontodon interaction

[lengthyfinger]

My opponent attempts to sacrifice his Thrashing Brontodon to destroy my enchantment. If I cycle my Nimble Obstructionist to counter Thrashing Brontodon's activated ability, will my opponent be able to activate the ability again (assuming he has the mana available) in response or will the Thrashing Brontodon be sacrificed and go to the graveyard without destroying my enchantment?

[Morganator 2.0]

Sacrificing the Brontodon is part of the cost. Your opponent cannot pay this cost twice, because the Brontodon is already in the graveyard by the time you're cycling Nimble Obstructionist.

[lengthyfinger]

Thanks for the help!

[Mnemosyne]

My opponent attempts to sacrifice his Thrashing Brontodon to destroy my enchantment. If I cycle my Nimble Obstructionist to counter Thrashing Brontodon's activated ability, will my opponent be able to activate the ability again (assuming he has the mana available) in response or will the Thrashing Brontodon be sacrificed and go to the graveyard without destroying my enchantment?

Don't forget to draw your card!