How much cash do I need to have to afford a $2M house?

Personal networth is just one aspect to consider when buying a house. 

You should consider cash flow from your work, your age and your material dream.

A) How much is your monthly cash flow?
Maybe be you don't have a huge networth, but if your job/busines provides a huge cash flow you can buy an expensive house even without the money in the bank.

B) How old are you? 
If you are young you can spend more in your house. Because your salary will probably raise over time.

C) Is this house your only material dream? Is it the most important? 
If yes, buy it as soon as you have the money.

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Saying that, rent is cheaper than buying a house. So, I would recommend you to check and do the math to see if it is cheaper to rent.

As a rule of thumb, never spend more than 30% of your networth in a house.

So for a $2M house, you need around $6M in total assets.