I agree, minimum $3000 all the way up to stupid amounts are possible. Alright, this is long, so I hope you enjoy reading it:
As people mentioned, moving to FX, the "investment" is in the lenses, the "cost" is in the body. Most of the value IS in the lenses, they work on the DX cameras too, and they hold their value especially if you buy refurbished or good used lenses.
Perhaps get the good FX lenses you want now, they will work on the DX, and you're much closer to the quality you need, pushing the capability envelope a little bit with glass. They will generally focus faster, look crisp, better bokeh, work with lower light, and again, can be sold for what you bought it for if you do it right. The FX "trinity" zooms are the 14-24, 24-70, and 70-200. That's $8K in glass right there, depending on what you want to do. You can also look at some popular primes if you have a specific need, 24mm, 50mm, 85mm (big favorite), 135mm, 200mm, 300mm, etc. Depends on what you need.
Not that this is a great idea, but here's the story of what I did as things evolved:
For decades, I used a film SLR with a 40mm prime and an 85-210 zoom. Did everything i wanted. Then I got into the DSLR's... and it is a whole new story as I really enjoyed getting into the digital stuff.
Here's my cashflow for going from DX-FX over a few years. I went from a D300S ($1600) with a 50mm f1.8 ($150)... cheap combo, great for the HDR stuff i wanted to do... but limited obviously. Wanted to do some motorsports also, so I added a 55-200 VR DX ($150)lens - which worked really nice actually, but looked cheap I thought that more expensive lenses were better... then sold that 55-200 and went to a big 70-300 VR ($400) lens, not any better really, much bigger and better quality build, and this I used for a while, but for motorsports stuff I wasn't too crazy about the 300mm end of it... this was an FX lens though. Sold it and got the 70-200 f/2.8 VR ($1500) and really liked it, another FX lens. Got a 35mm 1.78 DX ($200) lens. Bought a Tokina $600 ultrawide DX lens, sold it, got a Nikon $800 ultrawide DX lens, sold it. Bought a grip ($200) Bought a D700 ($1800), didn't like it, bought another D700 ($1900), sold the first D700 and the D300S, DX lenses, bought a 14-24 f 2.8 FX lens ($1900)a nd a 50mm f/1.4 ($300)... still with me? There's a 1.4 TC and a 1.7 TC in there somewhere also ($400).
Went from a $2,200 DX system to a $6,200 FX system, which cost me an additional $500 maybe as I bought and sold a lot of stuff, that's the cost of learning what works for me.
I love the FX setup I have now. It's a pleasure to shoot with nice stuff, it really makes it easy. But it's a lot of big, and heavy, and there's a lot of cash tied up there. I could so easily double the $ it if I got the lens I really want, and then some.
Later, I looked at a second DX body, I bought a DX kit D5100 with an 18-55 VR lens, and another 55-200 VR lens, for a DX setup for $1100 total. When I travel for work, I take the DX kit with me to take some shots occasionally. I did this because I needed something compact and light. That $1100 system does 99% as good as the $6,000 system until I push the limits with sports or creativity. That extra umph... can cost so much more. That 85mm f/ 1.4 lens which i don't have does just a liiittttle bit more than I can do. That 300 f/2.8 I want but don't have can focus a little faster, reach a little farther and narrow the DOF even more. Ha, yeah, for another $7K!
I tried the 24-70 to get the "trinity" but the 14-24 was immensely more impressive at the 24 end... and I have the 50mm prime.... and the beautiful 70-200... so I didn't see a need to spend $1700 for it. Everything is a trade off.
In the future, I will probably not get the extra FX stuff I want, but get a D400 and an 18-200 ($2500) and sell the current DX kit. The D400 will work nice for travel with the 18-200, and als for motorsports with the 1.7X TC and the 70-200. The FX kit will be fine for everything else, and may upgrade the body in a few years to a D800 or maybe D900 by then.