What if you rely on one income and you don't have $10K in your checking? I mean, YMMV here, but for most people, I don't think they have $10K in a checking account.
We live on one income and don't have $10k in our checking. If I lost my job we'd cash out investments in our Roth IRA if/as needed for longer term funds, and could use CC's to tide us over short-term. We can withdraw all contributions without taxes or penalties and live completely off of that for at least a year with no income, several years if we picked up any side income by either of us at all during that period. One may consider this emergency money, but it is invested. If we have the horrible luck of ever required to withdraw it in a down market, oh well. It doesn't represent that much of our stache and the gains it will probably see by leaving it in investments outweighs the risks of pulling it in a down market.
Although, the real key is having a super low cost of living. Once we cut extras like helping DH's daughter with college (which we wouldn't do if unemployed), various savings, gifts, fancy food, home renovation projects, trips, etc, we could probably get by pulling little from the Roth for a long time as long as we brought in even a minimal income. For example picking up some work like waitressing, delivery pizzas, teaching classes at a community college, substitute teaching, etc, could allow this to stretch considerably considering how low our expenses would be. Even better, we'd be able to come very close to being able to completely living off of this type of low wage work completely and pull nothing if one of us were able to find enough to do it full time, or if the two of us were able to each do it for like 20 hrs a week.
I sleep very well at night knowing that all we'd need to support ourselves at a level very close to how we currently live would be two people each making an average of $10k a year (assuming as a family of three that we'd then qualify for very close to fully subsidized health care, and about $3k in the EITC) if we absolutely needed to. We probably wouldn't even need to use any other gov't programs although we'd probably qualify (eg., SNAP, etc).