Would eliminating coal be difficult?

No.

We'd need only about $1.6T of wind investment to completely replace coal in the US, and power all light vehicles.

How did I come up with that? Well, we generate about 50% of our electricity from coal, 220 gigawatts. Wind, on average, produces power at 30% of it nameplate rating, so we'd need about 733GW of wind. Wind costs about $2/W, so that would cost about $1,466 billion. Transmission might raise that about 10%, to about 1,613 billion.

That's actually in the ballpark of the cost of the status quo, all told, given how expensive coal plants are to build ($4-$7/W), and the cost of fueling them. It's less than the cost of the Iraq war, all told.

That's only 73GW per year over 10 years. That's quite comparable to the average amount of generation the US installs every year right now. We built about 8.5GW last year in wind alone, IIRC, and expanding that to 73GW wouldn't be that big of a deal.

No big deal at all.

If we were to go to a 100% electric economy wouldn't we need 5 to 10 times as much electrical generation?

Not really. Electrifying all light vehicles, which account for 45% of US oil consumption, would only require an increase in generation of about 17% (220M vehicles x 12K miles/vehicle x .25KWH/mile = 75GW) in overall generation (450GW).

Wind, on average, produces power at 30% of its nameplate rating, so for light vehicles we'd only need 250GW of wind (75GW/30%). Wind costs about $2/W, so that would cost about $500 billion. Transmission might raise that about 10%, to about $550 billion. That's only $50B/yr for 11 years.

PHEV/EV's won't cost any more than existing light vehicles - the average light vehicle in the US costs $28K, and you could certainly add a plug and a much larger battery for $4k.

The same thing applies to air-source heat pumps for space heating.

Electricity is much more efficient than oil and gas.