I think part of the reason for the discomfort is that the adjective 'likely' already has the ending associated with an adverb, so we can't create the adverbial form in the usual way, by adding 'ly'.
This means that hearers who are less familiar with its adverbial use can 'hear' it as an adjective out of place, when in fact it is correct as an adverb.
It's not alone in this respect. [EDIT I mean, it isn't alone in respect of the impossibility of creating the adverb by adding 'ly' to the adjective]. The other similar term that comes to mind is 'friendly'. It always makes me stumble because it feels like the adverb should be 'friendlyly'. We have to resort to a circumlocution like 'in a friendly manner' (or use an altogether different word). That's what a lot of UK speakers do with 'likely', but it isn't compulsory I think, given that 'likely' is accepted as an adverb.