Note that insofar as McConnell is caving, he is allowing a vote on a bill that Trump says he would not sign, apparently reversing McConnell's previous refusal to do so.
He is letting there be a vote on an (apparently) clean bill to re-open the government without extra Trump wall funding.
There is also going to be a vote on a competing bill with extra wall funding as well, though.
https://www.nytimes.com/2019/01/22/us/politics/government-shutdown-senate.htmlAnyway, sounds like we probably shouldn't expect immediate resolution, but if we are now getting votes on clean bills, eventually a clean bill should pass after sufficient time and pressure has passed.