The biggest economic problem of the 21st century will be low growth.  Excellent book on the topic: Capital in the 21st Century,

The gap between the poor and wealthy will rapidly increase as GDP decreases.  This is because wealthy holders of capital will be able to almost always earn higher returns on their capital than 2% GDP, for example.  Their gains will quickly add up and multiply and governments will not be able to keep up with social programs to mitigate the increasing number of poor people in our society.

Neither side of the immigration debate will solve the low growth problem: 
- Decrease immigration so that existing citizens will have more jobs.  However, businesses  must have more consumers, otherwise there will be no job increases, for anyone.

-Increase immigration so that there will be more consumers.  However immigrants will compete for employment, especially at the lower wage jobs and will bring us some costs to integrate them into society in initial years.