Groceries and gasoline become scarce, transportation of goods and people becomes almost impossible, financial systems stop working, markets crash. The government can't collect taxes, deliver the mail, or defend the coasts. The health care system collapses. Cities fall into ruin, suburbs become battlegrounds. Organizations that do not now rely upon sophisticated interconnected systems - gangs, third world countries, etc.
Everyday life becomes a nightmare.
For example, a one-day shutdown of a single bank might cause many people to withdraw money from many banks at once. Or a temporary gas shortage will trigger gas lines and resulting shortages. Such systems failures are not directly date-glitch related. Everyday life would be disrupted, institutions may totter, but most of the major systems, like food delivery and healthcare, are likely to shake, but survive. In this scenario, despite major cascading technological failures, surprisingly, humanity will find common purpose.