It depends on how long you have overstayed and on what kind of visa.
For work visas, such as a valid H1 after a layoff, an overstay of less than 180 days is considered out of status, where as more than 180 is seen as unlawful presence.
An overstay of more than 6 months and less than a year is subjected to a 3 year ban, where as an overstay of more than a year is subjected to a 10 year ban.
So depending on your situation, the consulate can be lenient towards an out of status or an overstay of less than 180 days and still approve a Green Card application whereas unlawful presence means automatic denial of your application and a ban will be given.