WASHINGTON  In the beginning, Senator Barack Obama was not entirely sold on Senator Joseph R. Biden Jr. And Mr. Biden told friends that he was pessimistic of his chances of becoming Mr. Obama’s Democratic running mate.

Over the course of two months, as the dynamics of the presidential campaign and world events shifted quickly, Mr. Biden’s stock rose through one of the most rigorous vice-presidential vetting processes that Democrats could recall. It was a process in which Mr. Obama applied intense secrecy, careful pragmatism and political input from a team of internal and external advisers that have guided his campaign from the start. And it ended Thursday with a phone call from Mr. Obama, who reached Mr. Biden as he was at a dentist’s office where he had taken his wife to have a root canal.

On Saturday, as the two men embraced before a crowd in Illinois, the new Democratic partnership made its debut. Yet in a moment that could have showcased Mr. Obama’s decision-making, his top advisers made a concerted effort not to disclose how he made his choice, instead choosing to showcase the life stories of the two men on the ticket and to present Mr. Biden as a forceful new critic of Senator John McCain, Republican of Arizona.

“It’s a very personal decision,” said David Axelrod, the campaign’s chief strategist, in a brief interview Saturday. “He approached it in a very serious, sober and reasoned way.”