No, they want them to stay so that we don't have to deal with them. Whenever a country tries to improve their situation and it doesn't please us, we tend to intervene, like in Nicaragua. With Mexico, we started NAFTA under the assumption of their neo-liberal economic model which caused the peso to collapse and created massive unemployment. Clinton had to bail them out for 49 billion dollars, and NAFTA continues to screw their country over. Mexico very much appreciates the dollars being sent back.
They may have broken laws, but they aren't criminals. Rosa Parks broke the law, but history vindicated her. Immigration laws are racist and unjust. By the way, while crossing the border maybe illegal, living and working here is a civil infraction. That's to say that according to the law, it's tantamount to jaywalking.
Now, that they take our jobs? Sorry bro, they're offered the jobs, for less pay, and under worse conditions, than what the average american would demand. Also, if you lose out to immigrants who work better and faster than you, for less pay and under worse conditions, that'd be the market for you. Everyone should have to be paid the same, leaving everyone to fight fairly for jobs. This isn't the case. Also, the Alexis de Toqueville Institution, a conservative group, concluded that immigrants produce as many jobs as they "take". Because many of them are young and have families, they spend their money on clothes and foodstuffs, which are labor intensive goods, creating employment.
Cubans are allowed preferential treatment because the policies were enacted to undermine Castro's rule, not because we actually think that all Cubans be given refugee status. As i've said, the US has been shady about that.
Yes, it IS easier to make money here... because NAFTA has stripped millions of farmers from their livelihoods, the neo-liberal model endorsed by the US caused an economic recession to get worse, and the US has jobs to offer with a huge economy.
Think about it, you have a family to care for, do you stay in your country where there is no hope in sight because a nation to your north has you by the balls, or do you go where the jobs and money are, to take care of your family?