I COMPLETELY understand! My husband and I are also on that road to being debt-free. Unfortunately, we have a long way to go since we were pretty dumb while we had 2 incomes and are paying the price (literally) now.
That being said, I've had very frank conversations about our debt-epiphany with our families so that they fully understand our commitment to our financial future. We even had to cancel a vacation with my SIL & BIL because we simply didn't have the cash to finance it without a credit card--and that wasn't an option. And for family get-togethers, we've made them potluck occasions instead of dinners out. Quite frankly, that's better for all of us financially and healthwise, too!
With my closest friends, I've also spoken very frankly about our debt situation and our enlightenment to get out. Not really to tell them "I can't go out because I have no money..." but more in a manner of letting them know what's going on in my life and this budgeting stuff is a BIG part of it right now! More like "So, have you read Dave Ramsey's Total Money Makeover book? Dear husband and I both did and wow, did it open our eyes to make some changes. Man, this budgeting thing is hard! I sure wish we had more $$ to do the stuff we used to do, but we're committed to following through on this. Next time we get together, what activities can we do instead of what we normally do that might fit better into our budget? Maybe I can save up to do X, Y or Z if we plan ahead enough."
With my closest friends, they've been extremely supportive. Our families, too. We all recognize that using money we don't have (i.e. credit cards) isn't a good idea. If these people are really your friends, they'll understand. And if they ever ask what you want for your birthday or Christmas, suggest gift cards to your favorite restaurants/bars so that you can meet them for dinner/drinks! Saying no to invitations can be really tough, but if they're aware of the path you're on, they'll understand. You could even invite them over for a casual dinner in exchange for your "no" to their invitation.
It's hard, but remember, this is TEMPORARY pain for long-term success!! It won't last forever, even though sometimes it might feel like it.
Best of luck to you in following through and getting debt-free!
(are you doing the Dave Ramsey Total Money Makeover? Just curious.)