In 1862 there was a constitutional crisis in Prussia. The King wanted to reform the army, and while erveryone agreed that such a reform was necessary the liberals and the King couldn't agree on how this reform should look like. When King Wilhelm I. tried to impose his idea the liberals did the only thing they could: they refused to pass the budget in the Reichstag. Thus the king had no money to impelement the reform.
As there weren't any articles in the constitution what to do in such a case the King simply dissolved the Reichstag and hoped the new house would be more conservative. However, the opposite happend and the liberal won a huge majority and continued their policy. Wilhelm didn't want to back down before the parlament but neither he had the stomach to disregard the constitution and the wish of the parlament, so he offered his abdiction.
This would have made his son Frederick III. king and he was far more liberal and would have come to an agreement with the parlament.
The nobles and the other conservatives were horrified at the idea because this would have weakend their hold over the army and set a precedent that the parlament was stronger than the king.
Thus they called for Bismarck which should convince the King not to abdict and to solve the crisis in their favor. And the rest is history.
But what if there weren't a Bismarck to save the day for the conservative forces? The exact reason is irrelevant, wether Bismarck is never born, dies earlier, doesn't become interested in politics or suffers a heart attack during the crucial time (no to improbable regarding his life style) doesn't matter.
Wilhelm I. would certainly abdict - he had allready wrote his abdiction speech, and his son would become king of Prussia. How would Prussia fare under a liberal king, and Germany without Bismarcks unification? Would there be annother unification attempt by the people like in 1848?