Bad analogies from both sides guys.
Yes, if we just work at securing the border its not going to do much. Some of the MAIN reasons people are coming in will still be present (jobs, services, etc) so the entire time you're working on securing that border (which will take time, especially if its a wall) you're having large amounts of people coming in and even afterwards there will be high reward to attempt to bypass that high risk of getting around it meaning attempts are still going to be high. Will it slow the influx? Yes. Will it stop it? No.
If we JUST cut down on their ability to get jobs and services that also isn't going to be effective. There are still other benefits and reasons to come over illegally and still the chance of getting jobs and things under the table, and with a weak border the risk of actually coming into the country is relatively low. So will it slow the influx? Yes. Will it stop it? No.
The answer is a combination of those two FIRST...actual enforcement of laws AND protecting the border. Enforcement of laws could happen and begin in earnest tomorrow if need be, thus potentially slowing the flow of Illegals into the country while defense is ramped up. Once the border is secured and some of the major incentives are severely reduced then you have the double benefit of it being high risk to enter AND high risk to stay, doubling your chances of giving incentive and reason why NOT to illegally come into the country.
At that point you've slowed the flow of people coming into the country, you've hastened the flow of people voluntarily leaving the country, and you have a better way to monitor the coming and goings of people. Its at that point, when the security process has begun to be done and the enforcement process has been in place, that you begin to go into the secondary issues such as deportation or a path to citizenship, revisions of our general immigration law, looking into reforming or creating new temporary visas, etc.
Protect the Border and Remove the incentives, THEN tackle everything else. Do both of those first ones together and you have a FAR better chance at successfully doing it than if you do either of them singularly.