He could ask for legislation to get rid of the H1B program. It will be an uphill fight as you can get H1B holders to work for a fraction of what Americans require. They’re just grateful to be here. Even living several to a rented room they are much better off than living where they came from. Their goal is to send money home to their families. While I feel for these people, they need to be home fomenting revolution against the elite of their country who are making it the cr*p hole that it is. America provides the safety valve for many cr*p hole countries. This is one reason Mexico is as bad as it is. The potential revolutionaries are all working here and sending money home. The problem is, they are making this country just like their country. Notice the Sharia no-go zones in Michigan.
Actuality he would just need to strictly enforce the provisions under the H1B program to the letter. 90% of them would just go away as companies would have to pay the aliens the same as US citizens.
Right now no one is enforcing any immigration laws.