Given the rather large historical 'illegal' population in America, many having both children and grandchildren born in America and the virtual impossibility of removing most of them, the logical solution is amnesty for those who have been gainfully employed taxpayers for at least ten years without any criminal record and an automatic citizenship hearing. For those in America less than 10 years, but more than five years without any criminal convictions who have been steadily employed and paying taxes, a path to citizenship. Under five years - deportation. This should be a one time offer and anyone who doesn't take it up or have records of unemployment beyond just a few months between jobs or a criminal record can and should be deported. Perhaps then, if both parties can reach a reasonable and equitable solution to the latent immigration problem, then voters should expect a bipartisan solution to the border issue - whether it be a wall, a fence or a high tech solution. If there is no spirit of compromise by either party, they should lose their protected status and people should be encouraged to find better representation.
As to those currently banging at America's door on the southern border, if a 'National Emergency' can be declared at the discretion of the President, then as a national emergency, aggressive attempts to enter the country can be deemed a military matter and armed forces can be deployed and authorised to capture and remove unlawful entrants with transportation available to send them back to wherever they came from. There should soon be more military personnel available for the task.
At the same time, legislation regarding those who employ unlawful migrants needs to be created that is necessarily harsh, making the risk of getting caught employing the undocumented (i.e. those who have no permission to work or live in America) not worth the financial reward.