1. I believe there actually have been terrorists caught who entered the US by crossing a land border... the northern one. (Maybe Scott Walker was right about where the wall should go? PS I'm Canadian.)
2. Many, if not most, undocumented immigrants in the US are people who entered the country legally on a tourist visa and then overstayed it.
3. If you want to deal with the caravans coming from Latin America, you have to understand why they're coming: because they're fleeing gang violence in their own countries. What fuels that violence? Drugs, because of the US's insane "War on Drugs". End that, and you sharply curtail the power of those gangs, which in turn reduces violence, which in turn reduces the number of people fleeing north.
4. At least a plurality of Americans don't want a wall and are blaming Trump for the shutdown, not Congressional Democrats.
5. Any physical barrier across the US-Mexico border would necessarily have holes, because otherwise it'd be destroyed by water. And the costs of maintaining such a barrier would be astronomical.
6. As for Democrats being "big spenders", at least a lot of their proposals are for things that would actually help the public at large--and would save money. When Republicans spend big, it's for things that don't, like illegal invasions.