Having spent 12 years at two different universities, and another four as a data analyst for HHS, I might be able to shed some light on the stupid, lazy government employees ruining all of your lives. For this, you need to understand that all federal programs, whether it be roads or food stamps, are administered by the individual states. Some states handle that administration better than others. Big states like California and Texas have the resources to develop highly professional state agencies, while small states can really struggle, sometimes choosing to outsourcing the service delivery instead.
First of all, the biggest problem in each case is the attitude that state employees are all stupid and lazy. This starts in state legislatures. Budgets are always tight, which means salaries at state jobs are significantly lower than private industry. So right off the bat you have self-selected a lower quality of worker. Half the time promotion to manager is based on seniority (they "paid their dues"), rather than achievement, though not always. I've been lucky to have had some very talented managers, in both technical skills and leadership.
Next, because the workers are perceived to all be idiots, you have layer after layer of checks and balances to ensure the lazy workers don't steal public funds. On one project with the unemployment commission we were shocked to discover a 16-step process to close one purchase requisition. Our analyst calculated each requisition cost $80 in labor and materials to process. That means a $12 box of pens really cost $92 (bad example, as they had an exclusive deal for office supplies). At some point all that bureaucracy to prevent theft costs more than the prevented theft would have, probably by a factor of 100.
Finally, you have the regulatory whims of the legislators themselves. The next time a politician is demanding required drug testing for welfare recipients (as an example) and you're screaming yeah at your TV, consider for a second just how much money that is going to cost to administer. First, you have to pay for the drug tests, because you can't ask a single mom of three kids on food stamps to pay $80 out of their own pocket. Next, you have to have all the bureaucracy to ensure testing centers get paid for those tests, people to accurately track the test results, and case managers to deal with the benefits recipients. And at state agencies, these kinds of requirements change EVERY SINGLE YEAR. We had one change where 15% of federal funding had to be used for a newly-created employment service category. It cost thousands of man hours to implement, because out of the blue we had to modify all of our systems and subsystems for new categories, new procedures, and new timesheet requirements. And no, the policy change did not include additional funding to implement (called an unfunded mandate).
In my experience, about 20% of state employees are the worthless slugs you'd expect. The next 60% are average people just trying to do their jobs, which they do satisfactorily. Finally, there are the 20% of the people who are rock states, who generally give a sh&t about their jobs, and do it for less money because they believe in the mission of their employer. This really is no different than any private employer I have had, though it is harder to terminate the slugs at a state agency because of all the regulation (which comes from lawmakers that you elect).
In my opinion, it would work much better if they paid competitive wages, and then empowered employees to make decisions. But that would require legislators to release their iron grip on the bureaucracy, which they would never do.