2013 USA Walker Cup competitor Todd White advances
(USGA/Chris Keane)

Daley, whose professional hopes were derailed by a back injury in 2004 and who regained his amateur status earlier this year, upended David Noll Jr., 43, of Dalton, Ga., 4 and 3, in his third-round match. He rallied earlier in the day by winning two of the last three holes to defeat Erik Heggelund, 30, of Seattle, Wash., in the second round, 2 up.

“I haven’t played in any tournament in almost five years,” said Daley, who last competed in a USGA championship in the 2001 U.S. Open, held at Southern Hills Country Club, in Tulsa, Okla. “It’s fun to get the nerves and feel the grind. I forgot how stressful it was.”

Scott Harvey, the championship’s top seed and co-stroke play medalist, lost in the second round to Glenn Przybylski, 48, of Frankfort, Ill., 3 and 1. Harvey, the defending U.S. Mid-Amateur champion, was a member of this year’s USA Walker Cup Team.

The U.S. Mid-Amateur Championship continues with the quarterfinal and semifinal rounds on Wednesday. The championship concludes with a 36-hole final on Thursday, Oct. 8, starting at 7:30 a.m. EDT.

The U.S. Mid-Amateur is one of 13 national championships conducted annually by the United States Golf Association, 10 of which are strictly for amateurs.

Schmitz, who won his Round-of-32 match against Joe Alfieri, 46, of Lutz, Fla., 1 up, is the highest remaining seed at No. 8 in the match-play bracket. In the third round, Schmitz won five consecutive holes on the inward nine to dispatch Philip Lee, 30, of White Bluff, Tenn., 4 and 3. He made a tricky, downhill 5-foot birdie putt on No. 11 and drew an 195-yard, 6-iron to within close range for a conceded birdie at the par-3 13th.

“I’ve made a lot of clutch putts,” said Schmitz, who advanced to the quarterfinals for the first time after having reached match play in 2011 and 2012. “I haven’t given away too many holes with my putter. I have made birdie and par when I need to and played consistent.”

Daley, the No. 13 seed and the only other one of the top 20 seeds to reach the quarterfinals, posted consecutive birdies at holes 11 and 12 to build a 4-up lead against Noll in the Round of 16. He sank an 18-foot putt on the par-4 11th and then struck a 7-iron from 173 yards to within 12 feet on the following hole.

“It’s like an endurance test out here,” said Daley, who was a college teammate of PGA Tour veteran Luke Donald at Northwestern University. “I can’t remember the last time I played 36 holes, let alone walk more than one round in a row.”

Brad Wilder, 36, of Fort Wright, Ky., will square off with Daley in the quarterfinals. Wilder defeated Mike McCoy, the No. 5 seed, in the third round, 3 and 2. He won three consecutive holes on the outward nine and never looked back.

“He drove it great and putted wonderfully,” said McCoy, the 2013 Mid-Amateur winner and a member of this year’s USA Walker Cup Team. “I just didn’t handle the short shots around the green and I didn’t adapt to the grass very well.”

Todd White, 47, of Spartanburg, S.C., reached the Mid-Amateur quarterfinals for the second consecutive year. White rolled to a 4-and-3 victory over Kevin Van Rossum, 37, of Hartland, Wis., in the third round. He went ahead for good with a 15-foot birdie putt on the par-3 fifth before winning holes 8, 9 and 10 with a birdie and two pars, respectively, to construct an insurmountable lead.

White, who played on the 2013 USA Walker Cup Team and won this year’s U.S. Amateur Four-Ball with partner Nathan Smith, closed out his second-round opponent, Travis Woolf, 27, of Fort Worth, Texas, 3 and 2, earlier in the day by draining a 45-footer for birdie from off the front of the green on the par-3 16th.

“I am self-taught with no lessons,” said White about what worked with his ball-striking. “Everything is trial and error. So if something doesn’t work, I tinker a little with it to see if I can find something that works.”

White will face David Bolen, 36, of Lubbock, Texas, in the quarterfinals. Bolen easily defeated 56-year-old Matthew Sughrue, of Arlington, Va., 6 and 4, in the Round of 16.

Marc Dull, who caddies at Streamsong (Fla.) Resort, also won two matches on Tuesday. The 29-year-old from Lakeland, Fla., rallied past Kyle Nathan, 31, of Glenview, Ill., by winning the last three holes for a 2-up triumph in the third round after having edged Mark Harrell, the 2007 U.S. Amateur Public Links stroke-play medalist, 1 up, in the second round.

Dull’s quarterfinal opponent, David Gies II, also works in the golf industry, at Quail Hollow Club, in Charlotte, N.C. Gies, the youngest remaining player in the field at age 26, cruised to a 6-and-5, third-round victory over Justin Young, who had advanced to match play after surviving a 22-for-2 playoff.

Joshua Irving, 29, of Dallas, Texas, rounds out the list of quarterfinalists. He defeated Joe Doody, 26, of Huntington Beach, Calif., 1 up, in the Round of 32, then took out Przybylski, 5 and 4, in the next round.

In Przybylski’s first match of the day, Harvey, 37, of Greensboro, N.C., held a 2-up lead through 10 holes before losing four of the next five holes. Przybylski, who was playing in his 13th USGA championship and fourth Mid-Amateur, went ahead with a 16-foot birdie putt on No. 14 and won the following hole with a two-putt par.

Harvey, who was trying to become the first player since Smith in 2010 to win consecutive Mid-Amateurs, kept the match going when he halved the par-3 16th with a 17-foot par putt. He would concede the match on No. 17 when he missed an 8-foot birdie attempt.

“He made four or five 20-footers and I only made one,” said Harvey, who has reached match play in all eight Mid-Amateurs he has played. “[I] couldn’t get focused, couldn’t get energized. Every day I wake up I am just so exhausted, it’s been a really long year. I am just tired.”

Quarterfinalists receive an exemption into next year’s U.S. Mid-Amateur, Sept. 10-15 at Stonewall Links, in Elverson, Pa.