I think we need to more or less open our borders.
Establish a clear, obtainable path to citizenship that includes civic service requirements. Make it hard work but obtainable for anyone willing to put in the effort, and they're taxed on any income while here. Immigrants to the US have a very long history of being (generally) hard working entrepreneurs who in the long run make our country stronger. In the short term there's almost always been some level of turbulence while they assimilate but in the long term we're a stronger people for it.
Anyone not willing to work for it can expect penalties harsher than the current non-penalty setup of deportation.