To add my two cents from another country where 'illegal' refugees are a hot topic and have been for many years.
Let me just say this; taking a stance of "JUST DEPORT EVERYONE" without taking consideration of the circumstances which drove a person to attempt to seek asylum/amnesty in another country is, in my opinion, heartless and inhumane.
Here in Australia, there is a lot of propoganda about this issue. The government regularly feeds us a pile of shite about 'queue jumpers'. They neglect to mention that there is no such thing as a queue when it comes to immigration. I am a first-generation Australian; both sides of my family emigrated from Europe and both sides were considered refugees at the time of their arrival.
They were lucky. They had passports. They were able to apply for the necessary visas. Their situation wasn't so bad that they had to flee at a moment's notice. But when they arrived, they were forced to live in intolerable circumstances in a hostel, with conditions only barely better than a prison. All because they used the word 'refugee'.
Just imagine how desperate you would have to be, how intolerable your living conditions, to leave your home in the dead of night and hope you aren't seen, and walk/hitchhike across the country towards the borders with nothing but the clothes on your back and a handful of possessions if you are one of the lucky ones.
Imagine how scary it would be to know that if you are caught, it isn't jail you have to be worried about, but whether or not you will live to tell the tale.
Imagine hiding in the hull of a creaky ship, or hiding in the back of a shipping container, squeezed in like sardines, for days, weeks or even months, without seeing daylight and only having meager amounts of food and water to sustain you.
Imagine the kind of position you would have to be in to consider this to be better than your current circumstances, being fully aware that you might not even survive the journey.
Surely it would be better for each case to be considered on it's own merits. A refugee is someone who is fleeing persecution or intolerable living conditions, regardless of whether or not they had the resources to ask permission to become a refugee first. The UN Refugee Guidelines recommend having an immigration policy that enables genuine refugees to be granted asylum as part of the immigration legislation, regardless of how the person entered the country in which they are seeking it. It recommends implementing a system that allows a timely processing of asylum claims and calls for an efficient and accurate means to investigate each claim and determine whether the person is a genuine refugee.
If it turns out they aren't, by all means deport them, if they are in breach of border control rules. But at the very least take the time to find out before you send them back to a potentially horrific situation.