Going into Wednesday's 17th stage, the 41-year-old is lying second overall, 28 seconds down on Vincenzo Nibali and after the Italian suffered badly on Monday's final Pyrenean stage, Horner believes that victory in Madrid this weekend is within reach.
"Everybody knows that. All it takes is one bad day (for Nibali) and anything is possible,” the RadioShack-Leopard rider said.
Sitting less than half a minute off the lead and with Spanish climber Alejandro Valverde a further 46 seconds adrift, Horner, whose best previous Grand Tour placing was ninth in the 2010 Tour de France, believes Nibali is vulnerable.
"Everybody knows that it's really a three-way battle for the win, with possibly (Spain's) Joaquim Rodriguez (fourth overall, 2:29 behind Nibali) also in the race," he added.
"But Rodriguez needs to make up a lot of time and three guys ahead of him overall to drop back.
"Valverde needs a small margin and two guys to crack. But all I need is a gap. Twenty eight seconds, that's all, and I can take the leader's jersey."
A former winner of the Tour of California and Tour of the Basque Country, Horner is hoping to target Nibali perhaps as soon as Thursday on the short explosive ascent to Peña Cabarga's summit finish.
"They tell me differences can be made there but I'm not sure, though, because it's probably the first time I'm doing that climb," he said.
Horner admitted that in a career dating back to the small American NutraFig squad in 1995 he had "forgotten a lot of the climbs I've done before".
However, the final and toughest mountain challenge up the Angliru on Saturday is "definitely unfamiliar to me. That one you would know if you'd done in the past, because of its history and its name."
Horner added that racing hard before the final climbs of stages was a solid strategy to beat Nibali.
"Because if you don't, you're not going to drop him," said Horner, who has already claimed two stage victories in this year's race.
"He's one of the best guys in the world, he's won the Giro d'Italia and the Vuelta here, his resume is quite good," Horner added.
"So if you want him to crack, you've got to make the race hard. If he gets there (the final climb) fresh, he's going to be impossible to drop.
"But it's like I said, all it takes is one bad day and anything is possible."
Wednesday's stage is a flat 189 km run from Calahorra to Burgos that is likely to favour the sprinters. Three hilly stages follow before the race ends in Madrid on Sunday.