Mr. Johnson, who is now deputy director for management at the Office and Management and Budget, said most people were stunned to learn that the percentage of politically appointed employees in the federal government is so small, a mere 0.17 percent of the civilian work force of 1.9 million.

Mr. Johnson, who is well regarded by Republicans and Democrats alike for his expertise about federal employment issues, said that there were about 1,000 senior positions in the federal agencies that required Senate confirmation. These are typically positions like assistant, deputy and under secretary.

In addition there are 8,000 senior bureaucrats in what is called the Senior Executive Service and by law, no more than 10 percent, or 800, of these managerial positions may be filled by political appointees. Finally, he said, an administration has some 1,500 jobs to fill, known as Schedule C slots, with salaries ranging from about $25,000 to $150,000. The lower end of this scale are those jobs that people traditionally think of as political slots  suitable, say, for some party leader’s niece who just graduated from college.

(That adds up to 3,300, not including hundreds of federal judges, diplomats and members of boards and commissions.)

“To have one or two political appointees for every thousand employees is not unreasonable,” Mr. Johnson said. “It’s actually a minimal number given that every new administration wants to bring its own initiatives and needs a fresh set of people committed to those new policies.”

The long odds of landing a position have probably contributed to the frenzy of job seekers trying to gain whatever advantage they can.

One person involved in the Obama campaign said she had been contacted for help on behalf of someone who was three degrees removed  a friend of a relative of a friend. The Obama person spoke on the condition of anonymity, saying that to do otherwise, or to name names, would simply embarrass all concerned.