Normally bubbly Jones was having difficulty stringing a sentence together as she rounded off a six-hour climb in the early hours of today, having inched her way up 360ft (110m) of Moonlight Buttress in Zion National Park, Utah.
It was the presenter's 37th birthday but there was little time for celebration as she then had to spend the night in a tent suspended from the rock face.
She said: "The truth is that all I genuinely want to do now is get off this wall."
Jones aims to climb 1,200ft (366m) in order to conquer the cliff, exceeding the height of the Shard, following three months of training on climbing walls.
"From climbing centre to that was one hell of a steep learning curve," she said as she neared the end of the first of three days of climbing.
"It didn't feel like that day was ever going to end really."
The huge amounts of energy needed to cling on mean she is burning up to 700 calories per hour as her muscles ache and her limbs get scratched and bruised, and she is unable to wash.
Viewers of her BBC1 show will be able to follow her progress as she does the climb to raise cash for Sport Relief with her Alex Against The Rock challenge, which will also feature in a special documentary to be screened by BBC1 on Sunday at 3.15pm.