The 35-year-old Wheatcroft only earned a start for the event through Monday qualifying but now sits at 10-under, holding the 36 hole lead over fellow Americans Jason Kokrak (69) and DA Points (71) who are tied second at nine-under.
England's Brian Davis (70) and former Open winner Stewart Cink (66) are joint fourth at seven-under.
World number two McIlroy will get the chance to continue to hone his wayward game before the US Masters after he ground out a two-under-par round of 70 to make the cut on the number at one-under.
McIlroy, a week from being deposed by Tiger Woods from golf's rankings summit, managed three birdies and just the lone bogey in a more accomplished effort than his opening round of 73.
"It was okay. It was definitely more consistent today than yesterday," McIlroy told reporters.
"I gave myself quite a few chances. It could have been a couple better, but, you know, it was an improvement on yesterday."
The Northern Irishman's season has been less than stellar, with the twice Major winner adding next week's Texas Open in San Antonio to his schedule as he seeks form ahead of the year's first major at Augusta National which starts on April 11.
Since signing a new equipment deal with Nike in the off-season, he has missed the cut in Abu Dhabi, lost in the first round of the WGC Match Play Championship and walked off mid-round at the Honda Classic when headed for another missed cut.
Mickelson needed three back nine birdies to also make the cut on the number.
Wheatcroft, who has been a US Tour member three previous times but currently has just conditional status on the secondary Web.com Tour, was excited to be in unfamiliar territory.
"Bogey-free so far, excited with where I'm at obviously," Wheatcroft told reporters.
"I just have to approach the weekend the same as I have through the first 36.
"I don't have to worry about the money list out here. I don't have to worry about my status out here.
"If I win, it's great. It's kind of a win or nothing. I just get to go play golf this week. Everybody else can worry their status on the PGA Tour.
"Hopefully I can make enough money to get either temporary status out here or if I win, that's obviously the goal."
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