A skeptical take via e-mail:
Re: ICE and absconders, pt. 2 in your post. The WH is probably confident that ICE can handle the situation because the Senate killed Cornyn’s amendment that would have made absconders ineligible for visas. If I read it correctly, Kennedy’s amendment, which was passed instead, removes absconders (and ID thieves and Social Security fraudsters) from the list of ineligibles. So, of course ICE can handle it, ICE has nobody to apprehend! There is no problem that the WH and Congress cannot define away.