There are lots of possibilities. One is to do one segment a year using whatever vacation you get. Or make a deal with your employer to carry over your vacation until you have enough to do it all at once. Or, if you can save up enough money to pay the bills, ask for time off without pay.
You mentioned finances. There's no substitute for saving up. It might take some time to save what you need, but it's worth it. It's possible to tour on limited funds, anywhere from $10 to $50 a day.
Family is typically the main responsibility you might have. Maybe you have kids or are taking care of an aging parent or your spouse can't live without you. One thing you can do with kids and spouses is to take them along, either on bikes if they are old enough, or in a support vehicle.
I see three main categories of people riding across the country: (1) young people between school and employment, (2) empty nesters who don't have kid responsibilities any more, some retired, some not, and (3) unemployed people between jobs.
One thing you can do now is to start a touring fund and put as much money into it each month as you can afford.
Keep dreaming. Set a goal and set a date to achieve it.