I believe a bit of historical context is needed. Between fiscal year 1977 and fiscal year 2015, Congress only passed all twelve regular appropriations bills on time in four years - fiscal years 1977, 1989, 1995, and 1997. Between 1976 and 2013, there were 18 times where funding was interrupted because of the inability to pass budgets or continuing resolutions. Government shutdowns occurred after 1980 as a consequence of rulings by then Attorney General Benjamin Civiletti subsequently requiring the Federal government to scale back services without actual appropriations (ref). The budgeting process is completely broken down. We may want to assign proximate blame for the most current shutdown but whatever argument is put forth, it is essentially meaningless in the larger sense.
The discretionary budget represents less than $0.30 on every dollar spent at the Federal level. Congress has essentially no control over more than 70% of Federal spending. While it may seem counter-intuitive, as the discretionary spending constricts, the incentives to play brinkmanship games appears to increase. With less money available to work out compromises, there are incentives to switch from win-win negotiations to winner takes all. And it is only going to get more pronounced as mandatory spending consumes more and more of the Federal Budget. By 2030, government shut downs will be meaningless since discretionary spending will be all be gone away.
I am concerned that this shutdown may last a while precisely because no one seems to think it will and because Donald Trump is in a position to not back down. Furthermore, much of the government will continue to function (Vox). He does not really care if it blows up the Republican Party. I will make a prediction. Like all predictions, it could be way off. I believe this will go on for weeks. The DACA issue and immigration were core stances for Trump. He will cater to his base. He has no reason to back down.