Nearly every president has said one thing during the election then changed their tune after taking office. If Trump does this as well, he will possibly lose his standing amongst his supporters. That said, this will be really nothing new in the world of politics. Time will tell if Trump sticks to his word.
Unfortunately, I think Trump will have to do something heinous to turn off his blind supporters. Maybe people are so fed up with gridlock that any change is considered preferable. Immigration was a hot button topic on his campaign trail and this will likely be supported despite the costs and futility of building a wall to further isolate our nation.
President-elect Donald Trump has called on Congress to appropriate funds to expedite the border wall construction. Trump says that he will ask Mexico to reimburse the United States for the border wall. Therefore, this will not hurt Trump's standing with his supporters. Trump's supporters are loyal and will support their president.
Trump was a symptom of a large group of the populace who were unwilling to back an establishment due to economic uncertainty and slow recovery since the 2008 banking crisis leading to political tensions based on the priorities of governments and exacerbated by a government who had had huge successes but also failed to meet promises. These sorts of failures added to an anti-establishment mentality and so its more likely that the vote was something bigger as Trump is not popular. Also, as a result of a two-party system, issues are fought around key areas and so others will be neglected.
I believe that Trump supporters will understand the reasoning behind his change in viewpoint. It is nonsensical to think that Mexico would be forced to pay for a border wall, because they are an independent nation. Despite this change, Trump supporters will continue to support his policies and push for change in the government.