Do Immigration Laws Authorize Offenders to Take a Mulligan?

Emma Lazarus created those words on the Statue of Liberty which asked us to take in immigrants as part of a national core value.  This value is the basis for many who believe that immigration into the US must be without borders or conditions.  Immigrants who are here illegally seek to have a 'Mulligan,' in which they can choose which laws to break, which is a choice most Americans do not make in their daily lives, which are controlled by so many laws.  So this begs the question as to whether those who violate our immigration policies should be given a 'do over,' when it comes to adhering to our laws.
The U.S. has  prided itself as being, "a nation of laws." So how do we law abiding types reconcile those who violate our immigration laws?  How do we deal with those who seemingly take advantage over our systems which leave us with lesser medical care, budgetary woes, and with other social issues caused by those who come from agrarian economies where there is no middle class, to our industrialized society? We, as Americans, were seen early on as having big hearts.  Alexis DeTouqueville commented on our collective goodwill as a core value that seemed to escape the Russians.  
Immigration no longer encompasses the slogan at the base of the Statue of Liberty.  Immigration, en masse, is a threat to the fabric of our modern country. California spends billions on free health care and education without reimbursement from the Feds.  We have issues about detaining crimials as raised by our mayor today.  We have a shortage of medical care in many areas. We have no countries willing to pay us to take on their citizens and our foriegn aid is not creating decent jobs for those south of our border.
Our country cannot take in everybody.  This is why we have immigration laws.  Should immigrants be able to avoid our laws?  We certainly cannot evade the rule of law.  It would be anarchy to do otherwise.  It appears that we simply cannot take in everyone's huddled masses, even if the first waves are children.  We need to take care of our own.  We need to provide our own with affordable medical care, decent jobs, and the prosepct that our youth can still achieve part of the American Dream.  We must make hard decisions and realize that our world of 2014 is vastly different that the US in the Nineteenth Century.  Americans are a proud sort and they should have the prospect of opportunity and should demand that they should first enjoy the fruits of our liberty.  We are a country of laws and they must be enforced not only for self protection, but also to set an example for the rest of the world. We need to encourage those south of us to develop their economies and to develop a middle class, which solidifies a country's economic structure.  We simply cannot turn our country into a borderless state.  We have thousands that have died for our country in recent years and part of their commitment was to protect the United States.  Immigration must be orderly and there must be a full commitment from the Federal Government to strongly enforce these laws and policies, while encouraging immigrants to use lawful means to contribute to our country and to adhere to our laws.