The ACA (Obamacare) has taken some of the fear out of job loss, since you can sign up for health insurance without fear of being rejected for pre-existing conditions, and should you be out of work for a protracted period your insurance premiums will be quite heavily subsidized. It was absolutely awful prior to this - if anyone in your family had medical conditions and you lost your job you would have little choice but to be uninsured until you got another job. One accident or illness and you'd likely lose everything, since a week in hospital is an easy $100k. Bigger companies have to offer you the option to continue on the work insurance plan, but you must pay the premiums + 10%, which is usually > $2k per month for a family.
However there are still big gaps. You can be fired with no notice, and your health insurance can end that very day - you'll have to cancel any appointments, start the application for an ACA plan and wait 4-6 weeks until the ACA plan starts. Don't get sick or injured during that 4-6 weeks or, again, huge, life altering bills will roll in. Also if anyone in your family is receiving regular treatment (e.g. chemo) you'll have to put that on hold while you get insurance sorted out, and then possibly change doctors if the new insurance plan has a different doctor network.
Many Americans plan their lives (jobs, marriages) around health insurance - it's been that way for so long they regard it as normal.