These are the days of teshuva - return; these are the days of the blowing of the shofar, to awaken us from our slumber. It is during these days that one can cry out to HaShem and be answered and forgiven. The Rambam writes of how teshuva atones for certain sins, but for harsher wrongdoings the Day of Atonement and suffering is needed, too.
Still, there is one kind of sin for which all of this is to no avail, and for which only the day of death can atone. That, of course, is a sin which contains an element of Chilul HaShem. Yes, Chilul HaShem is so severe that when an aspect of it is attached even to a small matter, one must give up his life and not transgress the commandment.
In the time of King David, his son Avshalom rebelled and proclaimed himself king. David and his men, who feared for their lives, had to flee Jerusalem. David thought that the people would be shocked at the distress he suffered at the hands of his own son. They would blame the Al-mighty for having dealt unfairly with him.
'Therefore,' David said, 'when I arrive at the top of the hill, I shall bow down to G-d in front of an idol, so that people will be under the impression that I am prostrating myself before the idol. They will then reason that G-d is punishing me for my sins.'
When David’s counselor, Chushai, heard of the king’s plan, he rent his coat, placed ashes on his head and voiced his protest: 'Why do you want people to think that you, a righteous king, bow before an idol?' 
King David of old would rather have had people think that he worshiped idols.


King David of old would rather have had people think that he worshiped idols.

David said: 'Better I should prostrate myself before an idol and they should say, "David is not the tzaddik we thought he was, and deserves his punishment," than to desecrate G-d's Name by declaring that G-d's ways are not just, that a righteous king was murdered by his own son.'
King David was willing to go to the extreme of having people think that he, David, worshiped idols, just to not have a chilul HaShem through him. To this extent one must check his deeds, to make sure that there is no aspect of chilul HaShem associated with them.
In the end, Chushai told the king: 'You need not worry that G-d's Name will be desecrated. You married Ma'acha - the daughter of Talmai, king of Gesher - who was a yefat toar (good-looking captive woman) - and HaShem placed the section of a rebellious son after the yefat toar to hint that in a marriage to a yefat toar a rebellious son is the likely product. Therefore, your suffering at the hands of your son will corroborate the truth of the Torah and the justice of G-d's ways.'
In any event, man must run as far as he can so that none of his deeds have a hint of chilul HaShem in them. At the same time, we must be equally concerned with the nation of Israel, and try our utmost to erase all aspects of chilul HaShem on a national level from daily life.
First and foremost, the Jewish people must leave the exile, as the Talmud teaches us: When the Jewish people go into exile, there is no greater chilul HaShem than this. Could there be a greater chilul HaShem than the Holocaust, with its cry: 'Where is your G-d now? Why does He not save you?' Let the Jew of the exile understand this well, for if one cares about not being part of this great chilul HaShem, let him leave now while he can. About this, G-d cries out to His children: "For My own sake, for My own sake will I do it, why should My Name be profaned?"
And in the Land of Israel, the daily rock attacks, shootings and rockets fired on Israeli cities are a great chilul HaShem, which must be stopped at once. And, of course, the great ongoing chilul HaShem on the Temple Mount, the holiest of sites, left in the hands of the infidels, as they play soccer and picnic on the site where the High Priest would enter on the Day of Atonement. The site of the Altar is defiled, as the Jewish people are content to worship a wall. The government in Israel must do all in its power to wipe out this horrible chilul HaShem, and all must help them in this matter.
King David of old would rather have had people think that he worshiped idols, just to avoid a chilul HaShem.
And you?