Assuming the musculature of the mouth is much like that of existing carnivores, for the most part, I am wondering:
If the muzzle is at all plausible with a large brain
If the muscles of the snout just be too heavy or large for the head
If any 'space saving' adaptations such as putting brain tissue in the spinal area would work
If the head would be too ridiculously large to support at all
This answer will deal specifically with the relationship between brain size and a muzzle. Viz., Is the muzzle of a carnivore plausible with a large brain? The simple answer is no. This can be demonstrated by looking at human evolution.
This will be a simplified picture of that evolution, but this should suffice to explain the general principles involved. Essentially over the period humans from ape-like primates to modern humans cranial capacity, i.e., brain size increased while the size of their jaws decreased. Our oldest ancestors possessed prognathous jaws or what can be called basically big jaws that stuck out from their faces. This is the equivalent of a muzzle. By comparison, modern humans have flat faces and small jaws along with a greatly increased brain size.
Essentially hominids with large jaws had small brains. As they evolved into humans brain increased and jaw size decreased. Basically cranial capacity was constricted by the large muscles needed to support their large jaws. Modern humans' big brains and small jaws were anatomical features that co-evolved to make us human.
Source: Human Evolution
In the early days of human evolutionary studies there was discussion whether hominids evolved their big brains first or if the size of their protruding jaws became smaller first.
The Piltdown Man forgery was an unfortunate distraction to progress in the understanding of human evolution.
The "large brain first" view received further support when the Piltdown fossils were presented to the world. While we now know that they are fraudulent, at the time (1911) they seemed to demonstrate quite clearly that early humans had a modern cranium atop an ape-like body. And since the Piltdown remains were found in England, they conveniently supported the prevailing idea that modern humans had evolved in Europe, rather than in Africa.
This made acceptance difficult that humans evolved from more apelike creatures that progressively lost their more apelike features especially their prognathous jaws and their acquisition of less muzzle-like lower faces.
Consequently, when in 1924 Raymond Dart recognised the position of the Taung baby (Australopithecus africanus) on the human family tree, his ideas initially faced considerable opposition. Not until more australopithecine fossils were discovered did his recognition of A. australis as a hominid gain credence. However, it is now accepted that the ancestors of modern humans evolved in Africa and remained there until perhaps 1.5 million years ago, when Homo erectus populations left Africa and moved rapidly across Europe and Asia.
Consider Australpithecus afarensis as an illustration.
The best-known member of this species is "Lucy" , discovered in 1974 by Don Johanson & Tom Gray and estimated to be around 3.2 million years old (afarensis lived from 3.9 to 3 million years ago). This is an important find as the skeleton is remarkably complete for its age (40% complete by some estimates, but this does not include the bones of the hands and feet), providing a wealth of data about her size, posture, and gait.
Generally their sizes in terms of body height and brain sizes are as follows:
Afarensis remains indicate that the species was strongly sexually dimorphic, with males much larger than females. The remains indicate that afarensis heights ranged from 107 to 152 cm, and cranial capacity from 375 cc to 550cc (AL 444-2, a large adult male).
With the following facial and cranial features:
The face and cranium of afarensis was ape-like: a prominent brow ridge, low forehead, and a prognathous muzzle that lacked a chin. The teeth are intermediate between ape and human: the molars are large and the canines, though much smaller than those of living apes, are larger and more pointed than those of humans. The shape of the dental arcade lies between the human parabolic form and the apes' rectangular shape, and the foramen magnum, while further forward than in apes, is not directly under the cranium as in humans.
Interestingly the rest of their skeletons show features much more akin to a modern humans' than an apes. Although there are indications that they spent time in trees.
A summary of the differences between our Australopithecine ancestors and ourselves.
Australopithecus
Foramen magnum more forward –Australopithecus is mostly bipedal but
relies on nuchal crest / neck muscles to keep head upright.
Homo Sapiens (us!)
Foramen magnum is centred under the skull – H sapiens is fully bipedal
with head balanced on spine.
Skull Human
rounded brain case (enlarged brain) with reduced sites for muscle
attachment, especially those used for chewing and aggressive facial
displays which are no longer called for.
Ape
Flatter brain case (smaller brain) which allows for greater muscle
attachment sites needed for aggressive facial displays.
Importantly a carnivore with a muzzle will need greater muscle attachment sites to support that muzzle and to give it the biting power that a carnivore needs to either devour its prey or kill them. This will mean carnivores will have smaller brains.
In summary, larger brains are not plausible for carnivores with large muzzles.
Would the muscles supporting the muzzle be too heavy or large for the head?
This seems likely, but it is highly contingent on the size of the muzzle and the size of the brain case. Both features are antagonistic to each other. If the carnivore had both a sufficiently big enough and a big enough muzzle, then the whole structure could be very unwieldy. This isn't plausible.
In summary, yes but extremely improbable.
The 'space saving' adaptations of putting brain tissue in the spine seems implausible. One, because brains should be as close as possible to an organism's main sensory receptors. This is a general rule of thumb biologically. Two, it doesn't seem like there's sufficient room there to house additional mass.
However, some of the larger dinosaurs did have secondary brains located on their spines. Otherwise they would have had coordination problems managing their large bodies. Possibly a series of secondary brains could be located along an organism's spinal column. This wouldn't make the creature smaller, but more likely better coordinated. Perhaps if its cortex was located in the smaller brain case needed by a carnivore, then other major neurological features of the brain could be in its secondary brains. Notionally, but not at all certain if this is biologically plausible.
Also, octopuses have a highly distributed nervous system that extends through their bodies. This suggests a brainy carnivore might have evolved to have a similar highly distributed nervous system. Then, again, only its higher executive functions might need to be housed in the smaller brain case required by a carnivore.
In summary, while additional brain matter located in the spinal area seems implausible, there are two possible models for the relocation or emplacement of additional or extended neural systems. Please note: the organism would be different from most carnivores we know. This is very hypothetical.
If the head would be too ridiculously large to support at all?
Actually it's the combination of a big brain and a carnivore muzzle that is, sad to say, ridiculous. This has been covered in the discussion to the second part of your question. The combination of a big brain and big jaws is inherently contradictory. No impossible, but so full of problems for the organism with other features to be a hazard to its survival.
If such a creature existed it would need other anatomical features to protect itself and to be able to support a massive head. Perhaps a bigger body with powerful musculature?
In summary, more improbable and implausible than too ridiculously large.
However, this is purely speculative. If your hypothetical carnivore had a radically different body plan from the types of carnivores we know on planet Earth, then it might possess an anatomy where the equivalent of a carnivore's muzzle was separate from its brain case. Once the muzzle and brain case are separate structures they can each evolve to considerably larger sizes. The result could easily be a sapient carnivore with both a big brain brain and big muscular jawed muzzle. It would look very strange indeed.
This answer has considered the possibility of an intelligent carnivore with a muzzle and a large brain in terms based on features found in human evolution. While offering some possibilities about how this arrangement might work, its conclusions are generally negative about this working in combination.
