Can Kierkegaard's Absurdism generally be labeled as "a rejection of self-evident propositions"?

You can label it anything you want. How absurd.

Yes : )

Yes and no.

It is probably more accurate to note that Soren Kierkegaard adopted "the sickness unto death" as his title based upon his awareness of Christ Jesus' statement "...this sickness is not unto death, but for the glory of God, that the Son of God might be glorified thereby," referencing Saint Lazarus' death.

This awareness or realization places Soren Kierkegaard's "The Sickness unto Death" as his analysis of a post-Christian-era event, akin to Nietzsche's "death of God" motif. It is not that Christians are no more, but that Kierkegaard and Nietzsche perceived society to be de-Christianizing or secularizing (our current term is "post-Christian").

Thus Kierkegaard is not per se the "possessor" of the absurdity of post-Christian secularism (i.e., the phrase "Kierkegaard's Absurdism" is doubly misleading or misinformed: Kierkegaard does not "own" "absurdism," and absurdity is not properly Deified with capitalization, unless one is idolatrizing).

Rather, Kierkegaard "The Sickness unto Death" is diagnosing the post-Christian, post-Saint Lazarus type of non-acceptance of "resurrection demonstration per Grace of Christ, Truth;" he is discussing the types of (European, in his focus) personal issues he sees in the non-Christian, European human.

The notion of "labeling" portrayed in the question extends to the notion of "self-evident propositions," which is quite distinct from Kierkegaard's position re self-awareness. Rather than adopting (presumably) a Kantian 5-sense data flow as "self-evident" (Kant makes clear that such "self-evidentiality" is illogical, if one is claiming to know only 5-sense data exists (i.e., there is Noumenon and Ding an sich, the noesis and illusion of two of Plato's four types of awareness http://en.wikipedia.org/wiki/Analogy_of_the_divide... )), Kierkegaard focuses on and categorizes three types of "despair" (presumably described by the erroneously-categorized "Absurdism") in those who are non-Christian; all three types of despair (not "absurdity" per se) are directly developed as a consequence of non-alignment with the Will of God: a) a kind of "unaware" despair (Saint Paul denies this, as any human will be in awe of the "starry starry skies and moral wonder within"); b) a type of "hiding from self-as-aspect-of-God;" c) an understanding that self-is-aspect-of-divine-Love but not able/not choosing to love (God). This last of the three human types of despair is the most significant type of despair Kierkegaard diagnoses and treats; and is the only truly "absurd," i.e. "plainly illogical," condition, as the human, knowing self is, and self-in-Love is Life, does not come to love as enlightened Self-interest (per various psychologisms Kierkegaard investigates, e.g. pride, lust, mere "intellectualism," etc.).

So, again, Kierkegaard does not "possess" (as in the misleading phrase "Kierkegaard's Absurdism") the plainly illogical anti-Christic, Self-defeating behavior he seeks to analyze in "The Sickness unto Death"); rather, he analyzes the types of "despair" a soul encounters as a direct result of denying God Is, Truth Is. So, if whomever is posing the question believes that "Kierkegaard's Absurdism" is "Kierkegaard analyzing out-of-alignment (from God's Will) despair," and if whomever posing the question defines "self-evident propositions" as dogmatic (i.e., less than the logical level of Kantian analysis of "a posteriori" data) materialism, then the question is "valid." Otherwise, a very misleading question (not to mention a seriously-inaccurate awareness of Kierkegaard). Imho, the only possible defense of such a question's position might be to argue that Kierkegaard's narrator, Anti-Climacus, is Kierkegaard's idealization of the Christian position re healing of despair. However, imho that is a weak argument, as Kierkegaard's Anti-Climacus examination, diagosis, and treatment of post-Christian despair as plainly illogical posits the only reconciliation of the Real and the human is for the human to agree with the Real or transfinite; there is no other solution, and Kierkegaard reinforces this notion e.g. when he writes of the Knight of Faith (e.g., "Fear and Trembling").