According to Google Dictionary, an emergency is "a serious, unexpected, and often dangerous situation requiring immediate action." An example of an emergency is you've lost a lot of blood because of an accident or unexpected violence and need immediate medical attention; your house is on fire and you're trapped inside. Your appendix ruptures. You're driving and get caught in a flash flood. You get bitten by a rattlesnake in a remote area. You slip on ice and fall unconscious in freezing weather.
What's not an emergency? Donald Trump's promise to build a Southern border wall. Let's point out that unauthorized foreign visitors peaked before the 2008 economic tsunami, and there are roughly 11 million of them. Of those, probably a quarter to a third originally entered the US legally (e.g., they've overstayed their visas). Of the remainder, a significant percentage are spouses and dependents; if anything, stricter border protection without a legal right to return discourages reverse migration and encourages workarounds to family reunification in the US. US-born children of unauthorized migrants are constitutionally citizens by birth and eligible for applicable benefits by equality under the law.
Let's also point out that we already have walls, particularly around populated centers at or near the Mexican border. Much of the border without fences/walls is inhospitable terrain, and hence the marginal benefits of expansion are, at best, dubious.
Federal policy which heavily restricts legal paths to immigration is much of the problem. When Eisenhower faced a similar problem, he embraced the legal bracero (temporary worker) program, and immigration arrests plunged by up to 90%. One of my east Indian friends told me he had to wait 15 years before he could arrive (on an H1B visa). Many legal immigrants have to wait years to be reunited with family members. If anything, Republicans like Trump and Cotton (AR) want to cut legal immigration quotas even further, including lower-skilled workers, even as America ages.
Trump has been hyping the purported statistics associated with unauthorized migrants, especially allegations of violent crime, welfare usage, etc. He seizes on every rare incident and promotes it out of proportional contexts (say, vs. native-born murderers). Keep in mind 11 M migrants are less than 4% of our population, and migrants are generally ineligible for federal welfare state benefits, even years into a legal residency.
I'm not going to paraphrase Alex Nowrasteh's brilliant summary here, comprehensively debunking Trump's absurd claim of an immigration "emergency", including tame crime statistics north of the Mexican border.
But even if you subscribe to the myth that immigration is a crisis (even as Trump heavily promotes refugee caravans which are statistically insignificant), unauthorized immigration has been an issue for decades; in fact Obama had a reputation of being a Deporter-in-Chief. It's been the status quo, not a recent contagion in the Trump Presidency.
More troubling is Trump's unconstitutional attempt to divert funds legally allocated elsewhere. Keep in mind he didn't get his funding when the Republicans held the House last term. But the hyped Master of the Deal hasn't been able (or willing) to cut a deal for funding from two different Congresses, an implicit concession that he didn't have the authority to do what in fact he is now doing. This is lawless; it voids the rule of law. And, in my opinion, it makes the case for impeachment.