Of course Mexico doesn't want us to build a wall as they aren't suffering by having millions of Americans crossing their border for opportunities only to find themselves draining Mexico because of government assistance.
They don't want a wall going up and preventing them the opportunity to get rid of dangerous criminals. This isn't only for the safety of their citizens but also not having the financial drain that crowded prisons would cause. Lastly, they love all the wire transfers coming into their country. The money is earned here but spent and taxed there.
Trump knows Mexico has been taking advantage of us and all Democrats have done is to make things better for them (NAFTA), without putting American citizens first. We have leverage in our relationship with Mexico because they have billions of dollars in surplus because of our trade relationships with them. You only have to read Trump's book: Art of the Deal to know that he never began a negotiation without first knowing how much leverage he had. Democrats sold out the American people for obvious reasons (votes), by placating Mexico at every turn; the party is over.