House Republicans put forth an immigration package Monday which proposes some of the harshest restrictions on migration through the southern border, virtually ending the right to asylum for anyone not crossing through legal ports of entry. Though Sen. Bob Menendez (D-NJ) has put forth a set of recommendations on immigration, as yet there’s no competing legislation to help manage an expected influx of migrants through the southern border this spring and summer. The GOP’s extreme border package — which includes an effort to impeach Department of Homeland Security head Alejandro Mayorkas — is unlikely to gain enough votes to pass with the Republicans’s slim majority, but time is running out…