I was just speaking with my mom about that (she's 71). Medicare coverage is determined by income. The $250,000 estimate is accurate if you are at the higher income bracket (over $85k as a couple). You can expect to pay about $10k a year all in (B-D) & supplemental insurance (there are a lot of gaps) for a couple. So $250k isn't too far off the mark.
Long-term care is not included in Medicare. This typically runs about $6k/month per person for a full care nursing facility. It's not uncommon to need this for a couple of years.
If you wanted to have money for all of this yourself I'd say that 3 years long term care for both of you ($450,000), plus another $250k to cover your Medicare costs is a reasonable budget. So about $700,000 all in. Most people won't have the money for that.
The typical American will draw down all their assets if they get into a long-term care situation. At that point Medicaid will kick in.
To qualify for Medicaid (financial requirements) you must be making less than $2,000 a month (individual) and they will draw down all your liquid assets to $2,000 (individual) except for your house (exempt up to $536,000). A lot of people will use a trust mechanism to put assets in their children's names to qualify for Medicaid without drawing down all their assets.