Here is an interesting quote from John Bunyan's work Reprobation Asserted.
CHAPTER 9.Whether God would indeed and in truth, that the gospel, with the grace thereof, should be tendered to those that yet he hath bound up under Eternal Reprobation?To this question I shall answer,First, In the language of our Lord, 'Go preach the gospel unto every creature' (Mark 16:15); and again, 'Look unto me, and be ye saved; all ye ends of the earth' (Isa 45:22). 'And whosoever will, let him take the water of life freely' (Rev 22:17). And the reason is, because Christ died for all, 'tasted death for every man' (2 Cor 5:15; Heb 2:9); is 'the Saviour of the world' (1 John 4:14), and the propitiation for the sins of the whole world.Second, I gather it from those several censures that even every one goeth under, that doth not receive Christ, when offered in the general tenders of the gospel; 'He that believeth not, - shall be damned' (Mark 16:16); 'He that believeth not God hath made him a liar, because he believeth not the record that God gave of his son' (1 John 5:10); and, Woe unto thee Capernaum, 'Woe unto thee Chorazin! woe unto thee Bethsaida!' (Matt 11:21) with many other sayings, all which words, with many other of the same nature, carry in them a very great argument to this very purpose; for if those that perish in the days of the gospel, shall have, at least, their damnation heightened, because they have neglected and refused to receive the gospel, it must needs be that the gospel was with all faithfulness to be tendered unto them; the which it could not be, unless the death of Christ did extend itself unto them (John 3:16; Heb 2:3); for the offer of the gospel cannot, with God's allowance, be offered any further than the death of Jesus Christ doth go; because if that be taken away, there is indeed no gospel, nor grace to be extended. Besides, if by every creature, and the like, should be meant only the elect, then are all the persuasions of the gospel to no effect at all; for still the unconverted, who are here condemned for refusing of it, they return it as fast again: I do not know I am elect, and therefore dare not come to Jesus Christ; for if the death of Jesus Christ, and so the general tender of the gospel, concern the elect alone; I, not knowing myself to be one of that number, am at a mighty plunge; nor know I whether is the greater sin, to believe, or to despair: for I say again, if Christ died only for the elect, &c. then, I not knowing myself to be one of that number, dare not believe the gospel, that holds forth his blood to save me; nay, I think with safety may not, until I first do know I am elect of God, and appointed thereunto.
John Bunyan, "Reprobation Asserted," in The Works of John Bunyan (Grand Rapids: Baker, 1977), 2:348.
Several things are to be observed in this quote from Bunyan:
1) Christ is to be indiscriminately offered or “tendered” to “every creature” because he died for all. When Bunyan says Christ died for “all,” tasted death for “every man,” and is the propitiation for the sins of “the whole world,” he clearly does NOT mean merely the elect by these terms (see his comment about "every creature" toward the end). The free offer is grounded on Christ’s unlimited expiation of sin. This is his first point.
2) The “heightened” damnation of some of the finally impenitent who heard the call as recorded in scripture underlines the fact that they were sincerely offered Christ. The completely sufficient remedy of Christ’s death was “extended” to them through the gospel call, but they refused it. If there is no real sufficient remedy for them in Christ’s death, then the aggravation against their sin would not be increased.
3) The free offer of the gospel is related to the extent of Christ’s satisfaction. Since his satisfaction is unlimited, we may freely offer him. If his satisfaction itself were limited, then we could not freely offer him, nor would grace really be extended to reprobates for the taking. In effect, they (the non-elect) wouldn’t be hearing “good news” (the gospel). Hyper-Calvinists reason from a limited expiation in Christ’s satisfaction to either 1) limited offers or 2) no offers of grace. Bunyan seeks to refute their first faulty premise by arguing that Christ died for every creature. He grants that it would follow that if the expiatory death be limited to the elect alone, then we couldn’t sincerely offer Him to all. It’s just the case that the bible teaches that Christ died for all, and sincerely offered to all on that basis. There are some “Calvinists” today who maintain both a limited expiation and unlimited offers. Bunyan would think they’re inconsistent, and he’s right. By limiting the expiation in their theology, they're opening the door to a "limited offer" or "no offers of grace" (Joseph Hussey) type of theology, even though they vehemently deny it.
4) The warrant for sinners to believe in Christ is not merely in God’s command that they do so, but also in the fact that God, through the gospel call, “holds forth his [Christ's] blood to save me.” Anyone, whether elect or not, can be assured through the revealed will of God in the gospel that He has an interest in saving “me” in particular (whoever you are), because God has given Christ to die for all, not merely the elect. If it were the case that Christ died only for the elect, Bunyan thinks that one would be left in despair, wondering whether or not they are one of the elect to whom God is offering Christ. One would be left without warrant to believe, and trapped in an endless labyrinth of introspection/subjectivism.