I suppose you have in mind these four places: Matt. 7:13, 14; 20:16; 22:14; Luke 13:23, 24. These, as far as I am aware, are the texts upon which pre- and a-millennialism tries to erect their doctrine of the fewness that shall be saved.
The passages in Matthew 7 and Luke 13 are parallel passages and already contain much of the answer in their contexts.
In the passage as found in Luke, whose Gospel is to instruct us in the character of Christ's perfect humanity, this warning is directly after two parables which express the pervasive success of the Gospel/kingdom of God on earth (cf. Luke 13:18-21). Those parables teach that the kingdom of God would have small beginnings but would one day fill the earth. If you have listened to the series I am doing on this topic, you have heard me recite many passages throughout the Bible that confirm this teaching of Jesus. Christianity began with a crucified Savior and all men (apostles included) denying him and, I believe Scripture teaches, it will toward the end of time have a millennium wherein the kingdom of God has become a great tree and leavened the three lumps (mixing parables).
Matthew, more so than Luke, has emphasized the wideness of the way to destruction, Luke only mentions the narrow, or strait, gate. This is a warning contrasting Christianity with other approaches to God. The word translated "broad" in Matthew 7:13 means "spacious" or "roomy" and carries with it the idea of living comfortably and without troubles. The words "narrow" and "wide," describing the gates are relative terms. In other words, these only derive meaning in contrast to one another. There are two paths, and the two gates, or doors, standing at the head of each, the straight and narrow and the comfortable and wide. In Luke's account, he uses the same word for "gate," as John uses in 10:9 to give a metaphorical description of Jesus, "door." So, Jesus is contrasting salvation through him with other paths of salvation. It is through much tribulation we enter the kingdom of God (Acts 14:22).
There are two other contrasting terms used in these passages, "many" and "few." Again, these are relative terms and give no real information as to the actual number of those saved. In Luke's account (which is the chronological Gospel, cf. Luke 1:3, he writes "in order"), this question is raised immediately after we are told that Jesus taught that the kingdom of God would fill the earth. Yet, at the time Jesus spoke, the church was still a "little flock" (Luke 12:32) waiting to receive the kingdom. In Matthew, the warning has been placed in a block of teaching expressing the difficulty of being saved and the ease with which men deceive themselves in this matter. The warning is for men to avoid taking the path that attracts the most and easiest attention of men.
At the time that Jesus spoke these words, it was historically true that neither had most of mankind been saved nor would most of the Jews to whom he preached then be saved. However, it shall always remain true that the preaching of Christianity will be wider than its reception.
The passages in Matt. 20:16 and 22:14 both rely upon the previous teaching. However, in these passages, there is an explanation offered. "Many" are called but "few are "chosen." The difference between the many and the few is that between calling and election. The call of the Gospel is always wider than its reception. Hence, the contrast. The reason is because not all who hear the outward preaching are elect of God. The Greek literally reads, "many are called, but few are elect." Throughout most of history, the contrast between the "many" and the "few" has been numerically significant. Yet, the contrast is what we might express by the words "more" or "less." More people are called, or bidden, less people are chosen. Even during the millennium, though the vast majority of men will be saved, the hearing of the Gospel will still be wider than the election of God. The difference is that during the millennium, though fewer will be elect than hear the Gospel, the number of the elect will be greatly increased so as to fill all the world. "The earth will be full of the knowledge of the Lord as the waters cover the sea" (i.e., everywhere).
Should we look to the parables of the wheat and tares or the ten virgins, we might conclude that the number of elect versus reprobate would be virtually the same. Yet, I am unware of any who seriously put forth tis view because it would entail a wrong interpretation and misusing of the parables. They were not taught to indicate the progress of the kingdom of God on earth (unlike those in Luke 13:18-21); they were taught to encourage other traits in Christians (e.g., watchfulness, in the case of the ten virgins; patience in rooting out hypocrites, in the case of the tares). Matthew, in his Gospel, also emphasizes the progress of the kingdom of God in the middle of teaching the parable of the tares (cf. chap. 13) because the certainty of judgment does not preclude the progressive growth of the kingdom.
If you consider that there are more people alive today than throughout all of human history and, presumably, this will continue to be the case during the millennium, then, if most people living during the millennium are saved, most people in history will be too. One thousand years of ever increasing mankind numerically being brought to faith is layering of twenty generations of men, each larger than the previous, being redeemed. Thus, in heaven, the number of the elect is a number no man can number (cf. Rev. 7:9). During the millennium, Satan will be bound so as not to deceive the nations (not simply individuals; I deal with this in a series I taught on national establishments of religion and why they are biblical and eschatologically important). Nations, in their national capacity, with their natural majorities, will be converted to Christ then. Until then, the church goes through great tribulation. And, after the millennium, the church will endure a short period of tribulation before the end.
More always hear than are saved. This is not, however, a concept that necessitates thinking the final number of the saved will be few. Less will be saved than heard the Gospel but, in the end, the overarching theme of Scripture is that Christ came to save the world not just a few scattered individuals. Just as all die in Adam, so all are made alive in Christ. Paul's point challenges credulity if he meant by "all" a number so significantly smaller than the number of people who ever shall exist that the mass of mankind is reprobate and counted for naught. It is clear the tree of humanity is to be pruned of its diseased branches but pruning does not entail cutting off the vast majority of the branches of a tree. If Adam was saved, then we should expect most of his offspring to share in the election of grace (a point to be determined eschatologically, in time; cf. 1 Tim. 2:6).
The importance of missionary endeavor is that this point cannot and will not be testified in due time, until all the nations hear the Gospel. When the seventh trump sounds, "the kingdoms of this world" shall become "the kingdoms of our Lord and his Christ."
To paraphrase William G.T. Shedd, we should avoid two errors: first, that all men shall be saved; second, that only few men will be saved. Living in the time in which we find ourselves, it is easy to fall into the second error. During the millennium, men will likely fall into a variation of the first error and the short apostasy at its conclusion will remedy that. In glory, it will be a great multitude of mankind, in contrast to the whole of mankind, that will join in the praises of God to eternity (cf. Rev. 19:6).
The preponderance of Scripture teaches the universal spread and acceptance of the Gospel at some point in history (for proof, listen to my survey of the eschatology of the Bible). Four passages, which represent two teachings, and the second of which is founded upon the first, seems to be a slender thread upon which to erect the doctrine of the paucity of the saved.
As a supralapsarian Calvinist, who believes in limited atonement, I place the sincerity of the Gospel offers in two considerations: First, in the fact that the entire action behind and constituting the incarnation is salvific, men were already condemned apart from Christ coming. Second, in the eschatological reality that most men will be saved. The idea that there is a sincerity, when you really intend most men will be lost, is contrary to all the universalistic passages in the Bible. God so loved the world but saved only a tiny number of men?!? The divine intention is stated throughout the Bible to save innumerable multitudes, nations of men, of which individual believers represent the first fruits. Christ did not die for every individual of mankind but he evidently died for a large enough portion of mankind that it could be considered the "all," "the whole world," "all men," etc. These terms make no sense, from an Augustinian point of view, without adopting some kind of "double-speak" wherein "all," "the whole world," "all men," etc. mean only a small, even parochial, portion of humanity. It appears that no more than one third of the angels fell (cf. Rev. 12:4; it may be less, this may not refer to the whole). Should we suppose that God, who made man in his own image, and the Son of God, who took upon himself not the nature of angels but the seed of Abraham, should have purposed to redeem a lesser percentage of men than angels were kept from apostasy? This seems to belie the claim that God's redemption of men is more exalted than his upholding and confirming of the elect angels (cf. 1 Pet. 1:12).