YOSEMITE NATIONAL PARK, Calif. >> Two fearless dreamers who have captured the nation’s attention with their monumental climb reached the upper ledges of Yosemite’s El Capitan late Tuesday evening, just a few finger holds away from history.

By Wednesday afternoon it’s expected they will have carved another historical notch into the shimmering white granite where so many of rock climbing’s famed feats have occurred over the past half century.

Tommy Caldwell of Colorado and Kevin Jorgeson of California are on the verge of becoming the first to use only their hands and feet to summit a 3,000-foot sheer piece of stone known as the Dawn Wall.

The existential, three-week journey is being described as the world’s most significant "free climb" — and has left the world’s best climbers in awe as the men hoisted themselves up inch by excruciating inch. It’s a climb so daunting that no one else in their sport had ever even considered it.

"They’re pushing the limits of our sport beyond what most people can even fathom," said Julie Ellison, senior editor of Climbing magazine.

After a mentally taxing struggle they could almost see the end of an odyssey that began with an improbable thought seven years ago. Since then they have worked tirelessly trying to find a way up the slippery wall that gets its name because it catches the Valley’s first morning light.

Anyone gazing up at the world’s largest piece of granite, like the dozen or so Tuesday evening standing in a withered meadow below El Capitan, might consider the men daredevils. But the label does them an injustice, said Jorgeson’s girlfriend Jacqui Becker of Santa Rosa, Calif.

"To call them thrill seekers is to minimize the profundity of their passion and commitment," added Becker, monitoring each move from the meadow. "There is absolutely nothing thrilling about spending six years hauling thousands of pounds of gear up and down a mountain in freezing temperatures. There is nothing thrilling about leaving loved ones to tackle a distant dream. There is nothing thrilling about rehearsing and practicing and studying the same holds over and over until you dream them."

For practical matters, the climbers established a base camp of tents a third of the way up the natural monument.

Caldwell, 36, and Jorgeson, 30, have shuttled to and from the camp by repelling with ropes before attacking a day’s section. They ate, slept and recovered at the camp as friends ferried supplies to them.

The men have climbed in the late afternoon and night (the granite becomes slippery in the unseasonably warm temperatures), using headlamps to illuminate their way while being filmed for a documentary.

While most of the 100 routes up El Capitan are considered routine with the use of climbing aids, the duo are relying on their hands, feet and wit to get to the top, using ropes only to prevent deadly falls.

"It takes both courage and vulnerability simply to give voice to the impossible dream," said Becker, who despite a fear of heights planned to take her first climbing lesson Tuesday so she could greet the men on the summit when they finish.

Mostly, it has taken a steely perseverance to stare down the impossible. A storm stopped the men from succeeding in 2010. Jorgeson suffered a broken ankle in a 2011 attempt.

This time, Jorgeson fell almost a dozen times trying to make the ridiculously difficult 15th pitch of the 32-section route.

El Capitan has been the centerpiece of rock climbing since it was first conquered in 1958. It’s the place virtually every reputable climber goes to earn his or her cred.

But the Yosemite Valley climbing pioneers didn’t think El Capitan was a realistic endeavor before Warren Harding and Dean Caldwell (no relation to Tommy) made the ascent while strapped in with climbing ropes and other aids.

"We didn’t consider climbing it — it was too much of an imaginative leap," famed climber Royal Robbins told author Daniel Duane in his book, "El Capitan, Historical Feats and Radical Routes."

"It was just a big, blank space like the middle of Africa was at one time."