The passage is either 1.79-82 or 80-83 depending on the edition:
Greenough's translation (as given on Perseus) of the bold passage: "Yet here, this night, you might repose with me, on green leaves pillowed..." In a 1990 article on this very passage, Christine Perkell interprets "Tityrus' invitation" as being made sincerely.Hic tamen hanc mecum poteras requiescere noctem
fronde super viridi: sunt nobis mitia poma,
castaneae molles, et pressi copia lactis;
et iam summa procul villarum culmina fumant,
maioresque cadunt altis de montibus umbrae.
My understanding, however, is that no invitation is actually offered. The force of poteras requiescere, I believe, is a sort of counterfactual - "you might have rested". Fairclough in the Loeb translates is this way: "Yet this night you might have rested here with me on the green leafage..."
I've checked in Gildersleeve and Lodge, where this use of the imperfect is called a "tense of disappointment" (section 254 Remark 2): "sometimes used in [modal-like verbs] to denote opposition to a present state of things: dēbēbam - I ought (but do not); poterās - you could (but do not). These may be considered as conditionals in disguise."
I don't have any commentaries on the Eclogues to see if there's any discussion on the matter. If anyone does, I'd be obliged if you could have a look for me...?
It's an important point because it determines whether or not Tityrus ends the poem in a sympathetic mood to Meliboeus or not. I have generally found Tityrus a disrespectful character, though I like Perkell's view that Meliboeus is something too much of a dreamer to be taken over-seriously. Like so many of the Eclogues, the abrupt opening and ending allow space for the reader to supply interpretation to make sense of the dialogue. But if I am right, then we should reject that Tityrus does invite Meliboeus, and that instead, his description of an expected feast is a sort of taunt or ridicule.