We've been pretty irresponsible financially most of our lives and are just now looking to buy our first home early 2014 (long story). My husband's credit is hopeless at this point. He has many recent derogs, and I'd rather not include him on the mortgage application. My credit isn't all that great, either. But I've been rebuilding on my own since May 2012 with some success. I figure by March 2014 (when one of my auto loans will be paid off), that I could seriously start the homebuying process.
Me:
$55k-$60k annual income
Same employer 12 years
Current scores in my signature
Him:
$50k annual income
Same employer 20+ years
Scores in mid-500s
My credit
2 medical judgments, to be paid off by summer 2013
6 collection accounts that will fall off this year
1 unpaid collection from Midland that I'm still trying to figure out. will fall off credit 2014
2 paid small collections (property tax and overlooked old cable bill)
My debt
Auto loan $4000 balance, final payment March 2014
Auto loan $11000 balance, unplanned new loan 12/2012 (son totalled the old car)
Credit card total balance $2100 as of today (plan is to pay off all cards with refund and store them in the sock drawer, with the exception of 1 card)
Starter loan $250 balance, final payment August 2013
First of all, is there a lender out there that would approve just me for a mortgage? I'm assuming I can't include my husband's income if I apply on my own. I know if I could get approved, it wouldn't be for much (I live around Washington DC). And by next year, I may only have about $7000 in savings. How likely is it that this whole homebuying situation would acutally work for me? Also, any homebuying programs for registered nurses? 
You could qualify on your own in 2014 but you won't be able to include your husband's income on the mortgage app; however his debts may need to be included and that can affect the max home price you can afford. The max you can afford given your income and assuming very little debt is $200K-$240K. If you apply jointly, the home price affordable essentially doubles. I know in DC, a little costs a lot, so you might want to consider working with your husband on his scores.
Cards: Orchard Bank ($1100) | Cap1 Cash Rewards ($2500) | Chase Freedom ($1000) | Best Buy ($2500) | Discover It ($1000) | Barclay Rewards ($2500) | Current scores: EX FAKO: 684, CK TU: 649, FICO EQ: 680, FICO TU: 698, FICO EX: 658 Happy Homeowner Since 2/6/13!
I forgot to answer your other question. You will need to call your local housing authority and ask if there are any programs that you qualify for. Also if you are a member of a credit union provided through your employer, there may be programs there that you qualify for also. It best to do some research before heading to see a Broker because there are a lot of great programs out there that many people don't take the time to find out about.