Late payments in and of itself won't disqualify you from getting approved, provided your current credit scores are high enough, you've gotten caught up on the lates, and they were isolated incidents rather than a recurring pattern of disregard for your liabilities.
However, a lender would have to review your credit profile as a whole in order to make any determination. If the credit cards got charged off or sent to collections then it may take a little longer to get you eligible.
In any case, you'd have to speak to a lender directly to find out for sure if you can be approved.
I can assist you with this. Feel free to give me call or email me at your convenience.
Tony Grech | Mortgage Loan Originator | NMLS 977416
PMAC Lending Services, Inc.
Direct (248) 728-0078 | Fax (248) 595-7130 | Cell (313) 622-7383