I don't understand why would federal officials or congresspersons in the US succumb to lobbyists' requests unless they have skin in the game. How do lobbyists, I mean legal ones, persuade legislators or administration officials to pursue one course of action or the other (especially since they would understand that the lobbyists are driven purely by money and not genuine concern regarding how they could perform their duties better)? What leverage do lobbyists commonly use / can use?
The mechanics of lobbying can work at several levels.
"Senator, I represent the National Association of Flute and Tuba Manufacturers. Were you aware that flute and tuba manufacturers are the fifth largest employer in your state? Could I have 20 minutes of your time to present a white paper about the importance of tax policy X for the health of flute and tuba manufacturing industry?"
"Senator, I represent the National Association of Flute and Tuba Manufacturers. As you are well aware, the flute and tuba manufacturers are the fifth largest employer in your state. We'd like to invite you, and several other important policy makers to a presentation about the importance of tax policy X for the health of flute and tuba manufacturing industry. The presentation will be at Country Club Z. Dinner, overnight accommodation, and transportation will be provided."
"Senator, I represent the National Association of Flute and Tuba Manufacturers. As you are well aware, the flute and tuba manufacturers are the fifth largest employer in your state. Members of our association contributed over $1,000,000 to your re-election campaign. Could I have 60 minutes of your time to present a model bill implementing tax policy X, which is critical for the health of flute and tuba manufacturing industry?"
Finally, if the Senator seems unsympathetic to the interests of the National Association of Flute and Tuba Manufacturers, they could form a political action committee (PAC), that can funnel money to the election campaign for the Senator's opponents, or directly into negative ads against the Senator.
A legitimate lobbyist is paid to explain the needs of some special interest groups to the politicians. And also how the needs of that special interest group benefit the electorate as a whole, or at least not harm it. Less savory means include the bundling of donations from multiple sources for improved impact.
Say there is a slump in the dairy industry. A dairy lobbyist might draw up a detailed proposal for increased school milk schemes, ask parent-teacher-organizations to endorse it, find prominent physicians to speak on the importance of milk for children, and finally point out that farmers are voters. They might also give donations to politicians who favor the scheme.
No individual dairy farmer could do that. They're busy looking after their cows. But if thousands of farmers chip in, they can pay a professional spokesperson to do the job for them.
There are various ways how this legitimate pattern can become perverted, e.g. when ex-politicians get well-paid jobs in lobbying firms or when lobby groups provide detailed proposals which the politicians cannot even understand. This has been a problem with financial regulation and taxes, and the same consultancy firm working for politics and industry.
I'm Canadian so I only have a vague idea of how lobbying is done in the US but I recall one segment from a documentary about lobbying in the US that genuinely shocked me - and still does. The segment depicted the lobbying process in one of the state legislatures. If I understood correctly - I saw this at least 20 years ago - a normal session of the legislature was in progress and the lobbyists were literally sitting at small desks on the floor of the legislature and talking to legislators one-on-one. The legislators were apparently debating a bill, at least in theory, but they were mostly dropping over to the lobbyist desks and listening to the lobbyist argue why they should vote for or against the bill. I believe these lobbyists were working for industry groups but I suppose that's no worse than if they were working for other pressure groups. It was a long time ago and I don't remember the gist of the arguments or whether campaign contributions were mentioned but I was appalled that the lobbyists were right there in the legislature making their pitches and (metaphorically) twisting the arms of the legislators. It struck me as very unfair since presumably normal citizens did not have the same kind of access to the legislators.
This may well be naive though. I think lobbyists meet with politicians behind closed doors in my country because open displays of arm-twisting would be thought unseemly. Having the same discussions behind closed doors is really no less concerning than doing it during a legislative session. It still seems to imply special access for representatives of powerful groups.