Calvinism: Does God force people to be saved?

The word "force" is not usually employed by Reformed theologians when describing God's action in regeneration. We'll see why this might be in a moment, but first I'll give one counter example. B. B. Warfield was a leading Calvinist around the turn of the 20th century, and he wrote:

It is not true that "God forces salvation on no man." It would be truer to say that no man is saved on whom God does not force salvation,—though the language would not be exact.

It seems that Warfield's difficulty with the word "force" is that it seems to make too much of the dead soul's abilities:

It is not true that God's free gift of eternal life to His people is only an "offer": it is a "gift"—and what God gives He does not merely place at our disposal to be accepted or rejected as we may chance to choose, but "gives," makes ours, as He gave life to Lazarus and wholeness to the man with the withered hand. It was not in the power of Lazarus to reject,—it was not in his power to accept—the gift of life which Christ gave him; nor it is in the power of dead souls to reject life—or to "accept" it—when God "gives" it to them. (source)

The word regeneration, by definition, means "to be generated [made alive] again." We would not normally talk about God "forcing" a baby to become alive in his mother's womb. Nor would we normally say that God "forced" Lazarus out of the tomb (to use Warfield's example).

Why not? Because we recognize that unliving things/people don't have a "will" in the normal sense. And that's exactly the point: the "will" of a spiritually dead person is analogous to the "will" of a physical corpse. In order for either one to be made alive, God must act, unilaterally.

R. C. Sproul makes this point in his book Chosen by God by addressing a shortcoming he perceives in the frequently used evangelistic analogy of the "terminally ill patient":

The sinner is said to be gravely ill, on the very brink of death. He does not have it within his own power to cure himself of the disease. He is lying on his deathbed almost totally paralyzed. He cannot recover unless God provides the healing medicine. The man is so bad off that he cannot even stretch forth his arm to receive the medicine. He is almost comatose. God must not only offer the medicine but God must put it on a spoon and place it by the dying man's lips.

Unless God does all that, the man will surely perish. But though God does 99 percent of what is necessary, the man is still left with 1 percent. He must open his mouth to receive the medicine. This is the necessary exercise of free will that makes the difference between heaven and hell. The man who opens his mouth to receive the gracious gift of the medicine will be saved. The man who keeps his lips tightly clenched will perish.

This analogy almost does justice to the Bible and to Paul's teaching of the grace of regeneration. But not quite. The Bible does not speak of mortally ill sinners. According to Paul they are dead [Eph. 2]. There is not an ounce of spiritual life left in them. If they are to be made alive, God must do more than offer them medicine. Dead men will not open their mouths to receive anything. Their jaws are locked in death. Rigor mortis has set in. They must be raised from the dead. They must be new creations, crafted by Christ and reborn by his Spirit. (115)

So, to the Calvinist, does God "force" regeneration? Not in the usual sense of the word, because when we think of "forcing," we think of an active will being surpressed – not the "will" of a corpse. But the word is accurate insofar as it expresses that the sinner is a passive participant in his own regeneration – God acts upon the spiritual corpse without seeking its permission or requiring its cooperation.

Summary:

Traditionally, Calvinist / Reformed Christians have not viewed the process of regeneration as God "forcing" a person to become a Christian, since although God alone is the initiator of the process, the person being regenerated cooperates with it, and also because the word "force" has a misleading negative connotation given that salvation is a restorative and liberating process, while "force" typically implies the application of constraints.

This is a mystery that can't be fully explained but relates to the overall mystery of how divine sovereignty and human responsibility relate.

Note: I noticed you appear to be asking two related questions. I've primarily answered the word about whether Calvinist would say people are "forced to be saved against their will", and why Calvinists would deny that.

I've not discussed as much your question of whether effectual calling forces people to be saved some because they naturally were opposed to God prior to receiving the call. In brief, I would say that God does go against the will of the unregenerate in that sense, but that the unregenerate were created in order to find their delight in God (see Westminster Shorter Catechism Q1) so this is a deliverance for them from bondage to sin and so it is not a cause for criticism that God elects to go against their wills, since otherwise none could be saved (cf. Rom. 2-3)

Below I mainly discuss the mode of effectual calling, and why calling it God forcing us to be saved is misleading despite His sovereignty.

Details:

Regarding human will in general, Calvinists do believe people have "natural liberty" of will (Matt. 17:12, Jas. 1:14, Dt. 30:19) so that they are not "forced" to do good or evil. (Westminster Confession of Faith 9.1). This is not viewed as conflicting with God's eternal decree of "whatsoever comes to pass (Eph. 1:11, Rom. 9:15,18)": despite being sovereign, God is "not the author of sin (Jas. 1:13), nor is violence offered to the will of the creature (Matt. 17:12)" [all Scripture references from Confession].

Calvinists are commonly known as not believing in free will since historically speaking in the Reformation era, free will meant the soul had the ability to seek God and profess saving faith without the prior act of God in regeneration. (See Luther's work on free will for example.) Calvinists do not believe people who are not Christian have free will in that sense, since they are "dead in transgressions and sins" until Christ makes them alive (Eph. 2:1, 4-6, 8-10).

However, the Westminster Confession of Faith states that the "effectual calling" (the Spirit's inner call on the soul the makes the outer Gospel call salvific), which "renew[s] the will and by [God's] almighty power, determine[es it] to what is good" is one whereby people come most freely, being made willing by His grace."

The Scripture references that the Westminster Confession uses for the people coming freely are Song of Solomon 1:4 (with the King understood as being Christ), Ps. 110:3, John 6:37, Rom. 6:16-16.

Of these, Ps. 110:3 is cited most often by Reformed writers in this context. In Hebrew, it can be translated either as "your people shall be made willing in the day of your power" or "your people shall offer themselves freely in the day of your power": the mystery of salvation is that both are true. Ps. 110 is used both by Jesus in the Synoptic Gospels (Matthew, Mark, Luke) and by the author of Hebrews as a Messianic Psalm (a Psalm about Jesus). In the context of 110:3 it refers to the beauty of the King/Messiah. Traditionally, Reformed writers have taken this to mean that God reveals Himself inwardly in conversion in His moral beauty as infinitely worthy, and that this spiritual sight of Christ is of the essence of effectual calling.

Though in Reformed theology, people are "totally depraved", in the sense that their wills apart from God will always tend toward evil (self-centeredness and doing good for the wrong motives being forms of evil), they do believe that people are still made in the image of God, and thus we have an innate desire for something good, even though we pervert this desire into worship of the creature not the Creator (cf. Rom. 1). As St. Augustine, the great defender of monergism (God's sovereignty in salvation) said, "Our hearts are restless until they find their rest in You."

In effectual calling, God shows Himself, not your own self, not the creation, to be the only true source of rest, and the person who is being saved acknowledges the truth, since the "eyes of the heart have been opened" (Eph. 1:18). Their bondage to sin is taken away so they can freely serve Christ. The language of "forcing" is misleading here since people apart from Christ are the ones in bondage to sin, and God is restoring their wills in salvation to how they were originally created to be (though not perfectly until the Resurrection, WCF 10.5)

18th-century Reformed theologian Jonathan Edwards discusses at great length in his Religious Affections how salvation is based on a spiritual sight of the moral beauty and excellency of Christ. John Piper, who is highly influenced by Edwards, discusses this using the Eph. 1:18 and Room. 1 passages referenced above here: https://www.desiringgod.org/articles/how-god-opens-the-eyes-of-the-heart.

Finally, John Calvin himself said regarding John 6:44, "God's drawing is not violent, so as to compel men by external force" (Commentary on the Gospels). Puritan theologian John Gill said God's drawing is an "act of power but not of force".

The distinction is important here since an act of force would suggest a violation of the human person, whereas salvation as described in the Bible is actually redemption of them from slavery to sin, restoration of the image of God (a new creation), and enlightenment to the truth.

As it says in 1 John, "We love because He first loved us." God's love is the precondition for ours, but, because it is love, coercive words like "force" are misleading at best.

It is true that some Reformed people have even used phrases like "holy rape" to describe salvation. (Or more poetically expressed, the words of John Donne's "Batter my heart Three-Personed God".) However, I believe that this is due to their trying to resolve the mystery of how divine sovereignty and human responsibility relate, rather than being faithful to the balance of the Scripture's teaching.

I believe my citations from the Westminster Confession, Gill, Calvin, and Piper show that most people in the Reformed tradition would not use the word "force" to describe effectual calling / regeneration, due to it's connotations. God is in control, but the person being saved is cooperating as God's grace acts upon him or her.