Yes, we need a wall.  Why?  Because bad people sneak in without one.

They do with one too, but it's harder and thus there are fewer attempts, and even fewer successes.  That's good, not bad.

You have to want more illegal invaders to refuse physical barriers.  Just as locking your car or house does not make it impossible to steal from either, it increases the difficulty and thus makes it less-likely.  $5 billion in the context of the federal budget is just over one tenth of one percent of spending.  Any gain in security is worth that amount of money.

But if you want to stop the insanity generally you have to force Congress to keep the promise it made when Reagan gave amnesty to illegals: You must stop the handouts.

Reagan was promised wide-scale immigration reform to end the enticement to come illegally, on a permanent basis, in return for amnesty for illegals already here.  He gave Congress the amnesty.  He never got the elimination of the enticements and it was the Democrats that didn't give it to him.

This is the same political party refusing now and it does not matter that most of those reps and senators are no longer serving; the party itself is the same.

Trump therefore should demand, before any further negotiation, that the past promise be fulfilled.

It's not that hard to do:

• 100% E-Verify, under criminal felony penalty for failures to do so and business seizure for a second offense.  No exceptions.  This is trivially enforceable; employers already have to file 941s to report withholding taxes.  Add one field for each employee that must contain the E-Verify control number on each report.  Change the law so that non-reporting or false reporting on a 941 is a felony criminal offense with a statutory penalty of $5,000 per employee, per month not reported or falsified and that all directors, officers and employees involved in producing said false report are subject to a year in prison, consecutively, for each employee not reported.   This instantly ends employment capability for illegal invaders.
  
  
• No welfare or other government program of any kind that is in whole or part funded by the Federal Government (specifically: Medicare, Medicaid, Section 8, Food Stamps, WIC, S-CHIP, Education, etc) may be provided to any household unless all residing there are verified US Citizens or permanent residents.  Require prosecution for lies on said forms verifying eligibility and require that any such lie is a felony.
  
  
• No medical treatment without proof of payment is required of any facility except as pure charity care to any person who is not a lawful permanent resident or citizen.  All such care amounts, if provided without payment, must be publicly disclosed no less often than quarterly in aggregate along with the total amount of actual collected payments for services by all medical facilities (in other words if they're going to try to make you pay for it under the table they have to disclose it.)
  
  
• No remittances may be sent out out of the country without positive identification and proof of lawful residency or citizenship from the person doing the sending.  Period.
  
  
• No birthright citizenship.  Come here and crap out a baby, it's a citizen of whatever nation you are but isn't an American citizen.  You must be a citizen to confer citizenship at birth.  Period.
  
  
• Unlawful entry must be defined as a criminal felony and permanent bar to future entry for any reason.  If you wish to claim asylum, come to the border and lawfully request it.  If you wish to visit, come to the border and lawfully request entry.  If you cheat from this day forward no matter how or why you are permanently barred from ever entering the United States.
  
  
• Those nations which border ours must be held responsible for any person who is on their soil and makes an attempt at unlawful entry, or who is turned away or deferred during an asylum request until their case is heard.  If you are our neighbor and call yourself "friend" and "trading partner" then start acting like one.  If someone illegally enters from your nation you have a responsibility to take them back when we catch them.  If someone comes into your nation with the purpose of requesting asylum in our nation and you allow them to do that's fine, but that person's safety and place to live is on you until their claim is adjudicated.  What you do from there and whether you let the people in to make said claims in the first place is your business.  Any nation that refuses, even once, to take back an illegal invader caught after unlawful entry from their nation, or a person with a deferred or refused asylum request that presents at our shared border has all trade and border crossing closed until it accepts back the person or persons it allowed to attempt to invade our nation from their land.

For those already here who, the claim is, we should "take care of" (e.g. Dreamers, etc)

• If you came here as a child and are now an adult you must have graduated High School and demonstrate proficiency at a minimum standardized testing level in all applicable subject matter, including the English language, to qualify for further deferment.  While there are some "Dreamers" who are college students or even graduates at this point virtually all covered by this program are now adults.  ROUGHLY HALF have failed to graduate High School, demonstrate functional literacy in English or both.  These are not "Dreamers", they are public charges and must not be given anything beyond the theft they've already accumulated.  That one in ten -- or one in 100 -- is a high-achieving college graduate or student does not in any way extend to those who are either slugs or thugs.
  
  
• If you came here as a child and still are one you must complete your education and become proficient in English. Drop out or get kicked out and you both lose your eligibility and are immediately deported.
  
  
• You must have an executed Affidavit of Responsibility as for any other legal immigrant by an existing citizen who is responsible for you.  In other words you must have a citizen sponsor who both can and will take financial responsibility to prevent you from being a public charge.  This is required of legal immigrants and it damn well needs to be required here too.
  
  
• You must not have a criminal record of any sort more-serious than a routine traffic violation.  Any conviction for an offense against the public peace including robbery, DUI, drug dealing, shoplifting and of course more-serious criminal activity, whether by conviction or plea, is an automatic disqualifying event, without exception.
  
  
• You must document that you have either received all of your support from your sponsor or have lawfully worked and paid taxes in full.  This includes educational, medical and other government-funded expenses; if you received public education you or your sponsor must repay the fully-laden per-pupil cost of same.  If you received medical care under Medicaid or similar you must reimburse the full amount spent on your care by the government.  If you worked under the table you must demonstrate that you personally paid all the taxes otherwise due including both halves of FICA.  If you haven't done so up until now as a result of intentional conduct (e.g. working for cash under the table) you may be excused from criminal liability for your intentional conduct but you must report and pay all such tax arrears anyway, including interest and penalties as with any other intentional underpayment and you must begin to do so immediately and on an agreed payment plan without exception, or your sponsor must do so, until it is all paid off.
  
  
• Assuming the above is met you may have a provisional green card however you still go to the back of the line and are subject to all of the above until your turn comes up in our normal, legal immigration proceeding.  Once your turn does come up you may have full permanent residency and ultimately apply for naturalization as may any other lawful permanent resident.

That's the minimum opening requirement.

If we do not shut off the welfare state for illegal invaders we will never solve the problem.

Leave the government shut down until this is passed first.