Clearly there are already different answers to this. In fact the different answers are indicative of the problems of Buddhist karma. I've published two articles which touch on this question:
Did King Ajātasattu Confess to the Buddha, and did the Buddha Forgive Him? Journal of Buddhist Ethics. Vol. 15, 2008.
Escaping the Inescapable: Changes in Buddhist Karma. Journal of Buddhist Ethics Vol. 21. 2014.
The main point of the 2014 article is that the theory of karma changes over time. I trace one particular major change from the earliest records into the later records (and add some more speculative thoughts on the origins of karma theory).
Early Buddhists believed that karma must ripen no matter what. There is no escape from the consequences of one's actions. On the whole one's actions ripen as rebirth (punabhava). A few of them might ripen in this life as vedanā or sensations, and a few in subsequent lives (as rebirth or sensations), but most of them go to conditioning the next life. At least one Pāḷi sutta, Karajakāyasuttaṃ (AN 10.219; v.299-301), claims that in causing rebirth all unripened karma comes to fruition and we start each life with a clean slate. Though typically early Buddhists allow for karma to come to fruition after many lifetimes.
The only light in this picture is that through religious practices one can make oneself less vulnerable to the ripening of karma in this life (whether it was caused in this or a previous life).
However this changes. We begin to see more possibilities in the Theravāda Abhidhamma which invents a new kind of karma - upapīḷakakamma "counteracting karma - which can counteract or suppress the ripening of karma. Buddhaghosa, the great 5th Century father of Theravāda orthodoxy, is clearly still in the "Karma must ripen" camp.
For Mahāyāna Buddhists there are a whole range of religious practices one can do, including confession and dhāraṇī chanting, that can mitigate the effects of karma ripening, or even eliminate karma completely. Many of these are listed in the Śikṣasamucaya, a sūtra compilation by Śantideva (ca 7th or 8th century)
The difference is epitomised in the story of King Ajātasattu (2008) as found in the Samaññaphala Sutta. Having killed his father Ajātasattu experiences some uneasiness and goes to see the Buddha. After telling the Buddha what he has done and promising to be good from then on, the king leaves. In the Pāḷi version of the story the Buddha turns to the monks and says "Well, he's done for". Having killed his father even meeting the Buddha is not enough to save him. And indeed the commentaries say he went to Hell when he died. In the later retellings of this same story (ca. 4th-6th centuries) in Sanskrit and Chinese however, the king is miraculously saved by his meeting with the Buddha. The whole attitude to karma and how and when it ripens has changed. Karma is no longer inevitable.
The early Tantras, particularly the Sarvatathāgata-tattvasaṃgraha, take this to its apotheosis by introducing the 100 Syllable Vajrasattva Mantra (see also my Western Buddhist Review article on this mantra). This mantra, when chanted, is supposed to clear away any unripened karma, even of the most serious kind. Chanting it purifies all karma. Chanting it 100,000 times is a common prerequisite to receiving a Tantric initiation. Although it is interesting to note that at least one Tibetan group seems to be teaching the old story of inescapable karma.
Clearly there is no single "Buddhist" view on this question. Karma undergoes many changes over time and a number of mutually exclusive karma theories survive in the present. That said, I have yet to find any documented Buddhist teaching which suggests that karma will "balance out" in a single lifetime. The whole point of karma is that it is the mechanism that drives rebirth. And while many modernist Buddhists are dismissive of karma and rebirth, history shows that it was almost always a priority for historical Buddhists - I have informally written about a number of doctrinal changes in which the supposedly fundamental theory of dependent arising is modified to make for a better karma theory.
We also see that modernist Buddhists are apt to delude themselves about traditional Buddhist teaching. Buddhist ideas often suffer from ad hoc changes to bring it into line with psychology or modern views on rights for example. Rather than reject concepts which conflict with our values, we tacitly (perhaps even unconsciously) alter them to fit and then claim that this is what the Buddha intended.