2-4 million dollar inheritances are not common in the US and are solidly not "middle class".
In 2013, a household net worth of ~$1.87M was at the 95th percentile in the US (presented in a table here
https://en.wikipedia.org/wiki/Wealth_in_the_United_States#Wealth_distribution
but original data here
http://www.federalreserve.gov/econresdata/scf/scfindex.htm
). Let's examine a $2-4M inheritance based on this 2013 survey data. While I would be tempted to say that it's likely for a household to have a lower net worth at the time that an inheritance is passed on than it did at its peak because presumably 1 or 2 people have been living off that net worth without working for many years, let's assume that at the levels of net worth that we're talking about the household could very well be earning more income from investments than it is spending over that "retirement" time. Of course this depends on how people choose to live, and may vary across the range of net worths we are talking about, but we need to assume some relation here to move forward. So let's just assume peak household net worth and amount of inheritance passed on are equal.
The average married household in the US has ~2 children (https://www.census.gov/hhes/families/files/graphics/FM-3.pdf). This means that for an average individual (having 1 sibling) to have a 2-4 million dollar inheritance their parents would have to be a household with a net worth of 4-8 million dollars.
Using the calculator provided at (http://www.shnugi.com/networth-percentile-calculator/), which is based on this data, or looking at estimates like the one made here (https://dqydj.com/net-worth-in-the-united-states-zooming-in-on-the-top-centiles/), also based on that 2013 data, we find that in 2013, household net worths of $4-8M correspond to the 97.7 and 99.1 percentiles of household net worth in the US.
This means that an inheritance of $2M+ probably happens for about the top 2.3% of people in the US, with about 1.4% receiving something in the range of $2-4M. This actually seems quite high to me. Still, I would not say that this is at all "middle class". Most definitions of "upper middle-class" do not extend much into even the top 5% of the population. The top 1-2% is almost universally taken to be the "upper class" or the "rich" / "super-rich".
It does seem that people have difficulty classifying the group that exists from around the 95th to 98th percentiles, which exist somewhere between upper middle-class and rich. I would say whether a household feels "upper middle-class" or "rich" with a net worth in the 95th to 98th percentile probably depends largely on how much of their net worth is tied up in their primary residence. Still, OP isn't talking about even this group of people.
If we look at an inheritance of $10M - $100M as OP mentioned, we're talking about the top 0.2% of the population.
Interestingly enough, an inheritance of ~$50k implies a household net worth of ~$100k (for an average, 2 child household), which lands right around the 50th percentile mark for 2013. So a $50k inheritance is very much "typical".