If everyone starts out lost, why would Jesus need to seek? Isn't that like going to a forest and then seeking for trees? If "seeking and saving the lost" means what I suspect most people here think it means, wouldn't it have been more appropriate for Jesus simply to say, "I have come to save the lost?"
Luk 19:8 And Zacchaeus stood, and said unto the Lord; Behold, Lord, the half of my goods I give to the poor; and if I have taken any thing from any man by false accusation, I restore him fourfold.
Luk 19:9 And Jesus said unto him, This day is salvation come to this house, forsomuch as he also is a son of Abraham.
Luk 19:10 For the Son of man is come to seek and to save that which was lost.
Maybe you could tell us what you suspect most people here think that this means. I don't think (and certainly hope) that many here would dare suggest that Jesus ever mis-spoke.
A few things to keep in mind: 1) Luke 19 follows Luke 15, in which is recorded several parables about seeking lost things-- parables descriptive of salvation. This passage gives us an example of the seeking and saving work described in the earlier parables, stating that this is Jesus' purpose. 2) Verse 10 follows v.9, where a reason is given for his salvation-- "forsomuch as he also is a son of Abraham"-- that is a recipient of the covenant promises given to Abraham and his seed. Zacchaeus was a lost sheep that had wandered, a lost coin that had been found, a lost son that had been returned home. "Lost" here doesn't refer to all people in a general sense, but to those upon whom God had a unique, covenantal claim of ownership. This son of Abraham had strayed and Jesus sought him to save him, as He does for all His sheep. He doesn't lose one.
The reason this does not ring true for me is that you don't usually seek for everyone when we're all here in plain sight. You seek for something or someone among everyone -- in this case, the lost. Which raises the question, who are the lost? And why would the lost be a subset of everyone?
Eph; 1:4 even as he chose us in him before the foundation of the world, that we should be holy and blameless before him. In love 5 he predestined us  for adoption as sons through Jesus Christ, according to the purpose of his will, 6 to the praise of his glorious grace, with which he has blessed us in the Beloved.
The elect, who were elect before the foundation of the world were lost, He came to seek them and save them.
In this context, the lost refers to the not-yet-converted elect. Without knowing who these are, we proclaim the gospel to everyonel, knowing that He, by His Spirit, attends the preaching and proclamation of the Gospel to do His seeking and saving work.
So what you folks are saying is that this reaffirms the doctrine of election?
If a numbskull comes to the seminary and goes away a numbskull, do not blame the seminary.A. T. Robertson
I got to thinking about how the word "lost" is used in scripture. It almost always has a specific, not a general sense-- one that refers to those upon whom God has a unique claim:
Psa 119:176 I have gone astray like a lost sheep; seek thy servant; for I do not forget thy commandments.
Jer 50:6 My people hath been lost sheep: their shepherds have caused them to go astray, they have turned them away on the mountains: they have gone from mountain to hill, they have forgotten their restingplace.
Eze 34:2 Son of man, prophesy against the shepherds of Israel, prophesy, and say unto them, Thus saith the Lord GOD unto the shepherds; Woe be to the shepherds of Israel that do feed themselves! should not the shepherds feed the flocks?
Eze 34:3 Ye eat the fat, and ye clothe you with the wool, ye kill them that are fed: but ye feed not the flock.
Eze 34:4 The diseased have ye not strengthened, neither have ye healed that which was sick, neither have ye bound up that which was broken, neither have ye brought again that which was driven away, neither have ye sought that which was lost; but with force and with cruelty have ye ruled them.
Eze 34:5 And they were scattered, because there is no shepherd: and they became meat to all the beasts of the field, when they were scattered.
Eze 34:6 My sheep wandered through all the mountains, and upon every high hill: yea, my flock was scattered upon all the face of the earth, and none did search or seek after them.
Eze 34:15 I will feed my flock, and I will cause them to lie down, saith the Lord GOD.
Eze 34:16 I will seek that which was lost, and bring again that which was driven away, and will bind up that which was broken, and will strengthen that which was sick: but I will destroy the fat and the strong; I will feed them with judgment.
Mat 10:5 These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into any city of the Samaritans enter ye not:
Mat 10:6 But go rather to the lost sheep of the house of Israel.
Mat 15:24 But he answered and said, I am not sent but unto the lost sheep of the house of Israel.
About the only possible exception, that might refer to the "lost" in a general sense, is--2Co 4:3 But if our gospel be hid, it is hid to them that are lost: