The Midrash (Bamidbar Rabbah 14:1) presents several expositions of the following verses (Tehillim 60:9-10):
To Me is Gilead and to Me is Menasheh. Ephraim is the stronghold of My head, and Yehudah is My lawgiver. Moav is My washbasin. On Edom will I cast My shoes. Acclaim Me, Peleshes.
In one exposition, the Midrash interprets each clause as a proof against Hashem's critics. If you don't want to read through my paraphrase of the Midrash, a summary appears just before my question after the horizontal line below.
If you don't believe that HaShem can revive the dead, "To Me is Gilead" - Eliyahu from Gilead already did so, and he can bear testimony that HaShem can do the same.
If you don't believe that HaShem accepts ba'alei teshuvah, "To Me is Menasheh" - that is, King Menasheh, whose teshuvah was accepted in spite of such severe sins.
If you don't believe that HaShem remembers barren women, "Ephraim is is the stronghold of My head" - go to Elkanah from Har Ephraim, whose wife Chanah was remembered.
If you don't believe that HaShem abrogates nature for the righteous, "Yehudah is My lawgiver" - Chananiah, Mishael, and Azariah were saved from fire, and Daniel from lions, all of whom were descendants of Yehudah.
If you don't believe HaShem can heal people, "Moav is My washbasin" - go to Na'aman, who was healed through water, or Moshe, who was saved through water. (The Midrash explains why each one is called "Moav.")
If you don't believe HaShem can save from the gallows, "Upon Edom do I cast my locks*" - not only was Mordechai saved from the gallows, but it was thrown back at Haman, an Edomi.
If you don't believe that HaShem can save a person without a sword or spear, "Regarding Peleshes do they shout triumphantly**" - David defeated Golias without such weapons.
*The word "na'al" literally means "shoe," but the Midrash homiletically interprets it as being related to the word for "closing," and thus translates it as something which "locks" air out of one's lungs - a gallows.
**The phrase is "alei Peleshes hisro'a'i." On a simple level, the object is the speaker of the verse, and the subject is Peleshes, but the Midrash interprets the subject as an unspecified group of people and the object as Peleshes, based on a passuk in Shmuel Aleph.
TL;DR, the Pesukim in Tehillim 60:9-10 are interpreted in this exposition as various proofs that HaShem can (a) revive the dead, (b) accept repentants, (c) allow barren women to give birth, (d) abrogate nature for the righteous, (e) heal people from disease, (f) save from the gallows - and, further, place that decree on the one who issued it, and (g) allow one to win a battle without ordinary weapons.
To me, the common denominator is that HaShem can go against the usual nature of the world as He sees fit. Ordinarily, the dead stay dead, people must deal with the consequences of their actions, barren women don't give birth, fire burns and lions devour, the sickly die of disease, those decreed to die are killed, and the stronger of two combatants wins. The point of these Pesukim, it seems, is that HaShem can go against how the world normally runs as He sees fit.
If so, why do the Pesukim leave out other fundamentals, such as that HaShem punishes people for their actions (s'char v'onesh), that ordinarily a field only produces according to that which one plants, yet the righteous can get significantly more, as proven by Yitzchak Avinu (Bereishis 26)? Or that an enslaved, lowly, downtrodden people can rise to be the grandest of all, as proven by Moshe Rabbeinu when he redeemed the Jews from Mitzraim? Of all of the examples that the Midrash/passuk could have brought that HaShem abrogates nature as He sees fit, why did it pick on these seven?