I would not trust statistics quoted about illegal immigration one way or another. They are most likely propaganda. Many quotes say “immigrants have less crime”, for example, intentionally confuse legal and illegal immigrants. The other side often brings spectacular cases that may not be representative.
Legal immigration is much safer as people are to some degree vetted for their background and have known connections to people or companies in US. Congress should agree to the number we are willing to accept and stick with the numbers. If you want more, maybe organize private charity and sponsor more (may need some legislation also). Soviet Jews, arriving as refugees, were faring better in the communities that helped them directly, v. those that offloaded them to government services.
In extreme cases, like Syria, the most practical way to support refugees is to resettle most of them in nearby countries. Bringing 10,000 of them to US is taking focus away from the millions left behind.