Is the negative view that most Americans hold of the federal bureaucracy, justified? Depends on why they hold it. There are several valid reasons to hold a negative view. Some people may hold the view for other reasons, such as their favorite cause is not being "properly" funded. Some of the valid reasons are that 1) Government has no money of its own; before it can give to one party, it must take from another party. 2) Government cannot perform any function as inexpensively as private enterprise can. 3) The only function that everyone (nearly everyone) agrees should be perfomed by government, is protection. 4) A government bureaucracy never accomplishes the mission for which it was created, because if it did, it would work itself out of a job. 5) When government employees prove incompetent, instead of being fired, they are moved into a position where they do not have to do anything. 6) Here is a big one: Government agencies usually do not have competition for what they do, so they do not exert themselves to please the customer; they may be slow or rude or take only half measures, or all three. 7) Government employees often build unnecessary steps into their standard operating procedures so as to take more time and expend more money, thereby giving the appearance that they are very busy and doing important (expensive) work. 8) This one is connected to number 7; Each supervisor tries to justify more employees and a bigger budget, because the more people he or she supervises and the more money he or she manages, the higher will be his or her pay-grade.
I do not think that they view is justified, for the most part. I agree that the bureaucracy can be fairly inefficient at times. And I agree that it is too large. But it hardly seems fair to blame the bureaucrats for it. To me, it is the fault of Congress.
It is Congress that sets up the bureaucracies. Congress determines how big they will be and what their duties will be. Congress tends to make them too big and it tends to give them more discretion because it does not want to make the tough decisions.
So the bureaucracy has its problems, but to me it's because of how its set up and the political pressures on it, not because of the people themselves.
To find justification for this claim, I think you need to search for both quantitative and qualitative data.
Quantitative data would be information that is fact driven that can be proven by numbers from credible sources. I would research how registered voters are responding to the government right now. Yesterday was a primary election day. Usually primary elections have low voter turn-out. If more people are voting now, I think that justifies you claim. Look at if they are voting out the incumbents. That proves something even more.
Qualitative data would be testimonial information that has a genuine heartfelt opinion. I would interview 3-4 people with short questions that stab at answering your above question. If you have a "most" of your little group responding negatively, you have another piece of evidence that points you in the direction of justification.
People of a country holding negative views about its national governments is a universal phenomenon and not limited to America and its federal bureaucracy. This is partly due to the common human nature of being quick to find faults in others and overlook their merits. Partly is is also due to the fact that governments are very big organizations, which are inherently slow and cumbersome. This requirement of public accountability adds further slows down the work of governments by introduction of additional controls and checks.
Living in India, it appears to me that the Indian bureaucracy is one of the more slow and inefficient governments in the world, and in comparison the American system appears to be much better.