To rephrase, those whom Jesus dies for, He saves. Completely and utterly. No ifs, ands, ors, or buts. Obviously this is closely related to (U)nconditional election, as it is simply stating pointing out that people aren't saved by something they bring to the table, but rather by what Christ has done.
"Jesus saves!" is in opposition to the statement that might be offered up by those who believe in a universal atonement that "Jesus' death makes salvation possible to all who accept." Of course, this statement certainly is true from one perspective, if we affirm that those who accept have their hearts opened by the sovereign working of God (Irresistible grace anyone?).
Enough of throwing terms around. Let me defend the fact that Jesus' death secures salvation for those whom He died for, and the limited nature of His atonement will be established (as we don't agree with universalism).
4Surely he has borne our griefsIsaiah 53 is our classic "suffering servant" passage. C.J. Mahaney gave an excellent sermon on this text at Resolved (Have I raved about it enough yet?), and I just wanted to highlight one aspect of it.
and carried our sorrows;
yet we esteemed him stricken,
smitten by God, and afflicted.
5But he was wounded for our transgressions;
he was crushed for our iniquities;
upon him was the chastisement that brought us peace,
and with his stripes we are healed.
6All we like sheep have gone astray;
we have turned every one to his own way;
and the LORD has laid on him
the iniquity of us all.
Notice that in the text, there's no mention of potential. Everything is accomplished action.
Jesus has borne our griefs, carried our sorrows, was wounded for our transgressions, crushed for our iniquities, his chastisement brought us peace, and with his stripes we are healed.
... and the LORD has laid on him the iniquity of us all.
This language isn't saying that Jesus made possible salvation, it's saying that those he died for, those he was crushed for, those he bore God's wrath for, are healed.
tetelestai! (John 19:30) It is finished! Those that Christ has died for are healed. Are forgiven. Are bought. Perfected. Of course, this isn't separated from the rest of what Christ does as well. Those that Christ dies for will be given the gift of life, faith (through which they have justification), will persevere (we'll get to that), and all of this is sealed and accomplished by God. Jesus saves!
Another passage that is similar
11And every priest stands daily at his service, offering repeatedly the same sacrifices, which can never take away sins. 12But when Christ had offered for all time a single sacrifice for sins, he sat down at the right hand of God, 13waiting from that time until his enemies should be made a footstool for his feet. 14For by a single offering he has perfected for all time those who are being sanctified.v.14) By a single offering he has perfected for all time those who are being sanctified.
This offering isn't just a "maybe" but it's a "Yes and Amen!" Jesus' death perfects us. It saves.
And that's the story of the atonement. Jesus saves those he dies for. Not all people are saved. therefore, Jesus didn't die for all people. 
Two more things to address for this subpoint - "Is there biblical evidence that Jesus didn't die for everyone?" and the inconsistency of 4-point Calvinism.