All 49 Democrat Senators are supporting SB 3036, the first piece of legislation created to address this crisis. I'd say it's a pretty clean bill--read it yourself and judge:
https://www.congress.gov/bill/115th-congress/senate-bill/3036/text
While conservatives might decry this bill as "catch and release", nothing in that bill prevents authorities from detaining families at the border, or from detaining and separating illegals already in the interior of the United States (i.e. in cities with adequate resources.) Read it.
Republican Senators have also voiced support for the bill, or at least they had prior to their session with Trump and the introduction of 2 bills in the House. Let's see how things shake out, but I expect Trump will signal his displeasure (read: veto) for any bill that doesn't fund his wall.