Assuming election

The high Calvinist puts it like this: Christ only paid for the sins of the elect, so there is no actual way the reprobate could be saved, but this compromises the indiscriminate offer of the gospel. Their resolution of this tension always leaves something to be desired.  Grudem says this (and I couldn't help but embed my comments):

In answer to the objection that this compromises the free offer of the gospel to every person [I] answer that we do not know who they are who will come to trust in Christ, for only God knows that.  As far as we are concerned, the free offer of the gospel is to be made to everybody without exception.  (This is the main point I want to address.) We also know that everyone who repents and believes will be saved, so all are called to repentance.  (this is precisely what we don't know since we know Christ doesn't die for everyone. What we do know is that He has made a way for some only, who they are we don't know.) The fact that God foreknew who would be saved, and that he accepted Christ's death as payment for their sins only, does not inhibit the free offer of the gospel, for who will respond to it is hidden in the secret councils of God.  (This is not true, if God has not paid for their sins then that does inhibit the free offer because there is no offer)  That we do not know who will respond no more constitutes a reason for not offering the gospel to all than not knowing the extent of the harvest prevents the farmer from sowing seeds in the field.

Ah yes, we know you may be reprobate and therefore have no hope, but just believe, at which point you will find out it was meant for you all along.  Joseph Bellamy's explains the problem of this:

If I know that Christ died only for the elect, then I must know whether I am elect, before I can know if I'm saveable. 
But there is no way to know that I'm elect, since it's His secret decree.
I must first assume, for no reason, that I'm elected, before I can believe in His willingness and ability to save me. 
Once I have faith I infer I'm elected as the Bible instructs, and the circle is complete.

An example: Say I'm a dying wealthy gazillionare who has a wayward son. Since I'm not going to live much longer and I want to see my son one last time before I die.  I instruct my attorney to draw up a will that states if my son comes back I will install him as the heir, otherwise he won't get a dime. To get the word out I take out an ad on every media outlet, everywhere, all the time saying this: my son, my fortunes are yours if you come home.
Is that a valid universal offer? If someone who is not my son reads it what will he think? Will they assume sonship then try to take me up on my offer? No, the offer is only good for one person, and everybody knows it because I intend to pay for only one person.  Such is the problem of limited atonement, to be eligible one must first assume their election.