Looking at my book of cartridge dimensions...
The .30-40 Krag has a rim diameter of 0.545"
The .45-70 Government has a rim diameter of 0.608"
I just pulled the bolt out of my 1898 Krag to mike it. Mine measures 0.622" in bolt diameter. In other words, you'll have to mill off the entire face of the Krag's bolt flush in order to accomodate the .45-70.
And, as mentioned above, the gun would have to be a single shot affair - because there's no way on Gawd's green earth that the Krag's side box magazine and feedways are going to let the big .45-70 slip through, without some SERIOUS grinding and contouring. Took me more than just a couple minutes to get a loaded .45-70 round out of this Krag's box magazine, it got wedged pretty tight.
The Krag action deserves to run another .30-40, find a .308 barrel blank and have it fitted. If you don't like the .30-40, I've shot a couple Krags rebarreled to .30-30 Winchester, too.
For a bolt action .45-70, use a Siamese Mauser action (one of my current projects). Otherwise, Gibbs Rifle Company was selling rebarreled No4Mk1 Lee-Enfields in .45-70, too.