There's a difference between a sweeping immigration bill, and resolving a particular issue. You can address the migrant crisis without touching the third-rails of amnesty or employer restrictions.
I would think a humane bill for the migrant crisis would include the following...
- an increase in funding for immigration judges, so they can process claims faster.
- an increase in funding for Mexico to provide for asylum-seekers there.
- an investigation into wrongdoing and other problems.
- funding for higher standards in migrant centers.
- some kind of mechanism for emergency spending if there's an increase of asylum-seekers in the future.
- a higher standard than the "credible fear" standard for the first stage of asylum claims, since many of the people who meet that standard ultimately have their claims rejected.
- clear standards for judges on what merits asylum, so you don't have judges determining that any victim of domestic violence in Central America can gain asylum in the US.
As for what Republicans have currently done, there has been a sharp drop in migrant arrivals.
https://www.nytimes.com/2019/07/10/u...gtype=Homepage