To be fair, the administration has made several concessions (steel instead of concrete barrier, a multi step funding proposal, DACA extension, etc), while the Democratic leadership has been unwilling to compromise on increased funding for border security. It is on both sides that this shutdown has gone on so long.
The shutdown began under a government where all 3 branches were under Republican control when the Admin. refused a bill that had already cleared both houses, the Senate via unanimous consensus. So the shutdown is absolutely the direct result of the Admin. In regards to its continuation, were the Democrats to yield this would set a precedent that a shutdown can be used to force negotiation at gunpoint with real people used as hostages.
I really don't see how this is anything except an attempt for the Admin. to save face over a failed campaign promise to build a wall that would be paid for by another nation. The senate Republicans refusal to approve the same bill they unanimously voted for is the reason the shutdown continues.
[1] https://www.economist.com/united-states/2013/10/03/closed-un...
(It's also notable that neither party, politically, has a good reason to end it. Trump will have a hard time holding onto even his strongest supporters come reelection if he can't start the wall, the most tangible and physical representation of his promises to his base, and the longer the shutdown persists, the better Democrats will do in Congress next election, the shutdown is a political godsend.)
I don't think the democrats should cave because this is a terrible precedent that far outstrips "appearance". It feels like a perversion of checks and balances where, because on side doesn't get what they want, they shut down the entire government until the other side caves. I won't be a fan of future presidents shutting down the government every time they can't come to a bipartisan agreement.
Which is to say, one party is certainly responsible for picking this fight, but both parties are responsible for not ending it.
They are acting like children. If your son relentlessly bullied your other baby and in order for your baby to stop crying your son said "give me $5" (a meaningless amount to most adults) - the solution wouldn't be to give him $5 and teach him that whenever he wants money he just has to threaten throw the baby down the stairs.
If the clean CR fails, then its a terrible future ahead. In 2018, when Democrats were in the opposite situation (they were denying the CR), it was on the onus of the Republicans to push for the CR.
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The only reason why the CR is agreed upon in the past, is because both sides recognize the harm that a shutdown would cause. Unfortunately, one side is willing to shutdown the government and avoid the CR this time.
Trump has refused to accept continuing resolution proposals unless they include a down payment on the wall [1] - these proposals continue prior funding while the budget is discussed, alleviating the shutdown.
[1] https://www.washingtonpost.com/business/the-latest-2-dozen-h...