Mexico flat out refuses to pay for the wall. Unless, Trump wants to go to war over the payment of the wall, which Congress will refuse to allow, Trump has to soften his stance. Requiring another country to pay for American projects is unreasonable. Therefore, he will have to adjust his unreasonable stance.
He is a flip flopper and a smart talker. he will say that the wall idea was hyperbole, or flat out deny that it was part of his plan. Maybe he will eventually be caught in his lies. He will definitely go strong on the wall idea and he will definately back down.
Yes, Trump will soften his stance on the Mexican wall. He never expected to make Mexico pay for the wall. Like many things he's said, Trump talks without thinking, then chooses to continue with his ideas until he finds out he can't. The Mexican wall earned him votes and his tough talk was attractive to a lot of people.
I'm pretty sure that Trump's ego won't let him concede the idea that Mexico won't be paying for his wall. Do I think it will actually be built? No way! I imagine his inability to build the wall on Mexico's dime, or any wall for that matter, will be one of many pitfalls of his presidency and will ultimately make sure he is not reelected in 4 years.
I believe that Trump will not soften his stance on Mexican wall. Though the Mexicans seek cooperation, they still refuse to pay for wall. This might be the right thing to do but trump is an arrogant leader and he will not change his mind and favor the Mexicans in any way.