Just by itself, no. A green card is only proof of permanent resident status, it is not status itself. However, not having proof of permanent resident status will cause you a lot of problems because you are indistinguishable from an undocumented alien.
Failure to renew a green card is not by itself a ground of removability.
Renewing a green card is fairly straightforward. Talk to a lawyer who can allay any fears you may have if you're late.
As noted above, the card expires but the status itself does not - that's why it's called lawful permanent residence. Not having a valid green card can present problems - for example, if you are between jobs, an expired green card is not an acceptable I-9 document to prove your eligibility to work, so a new employer would not be able to hire you unless you renew the card.
However, there are exceptions where your status may in fact be endangered. For instance, if what you have is conditional residence (a 2 year green card) then the status does expire if you do not affirmatively file to remove the condition, and you are removable if you fail to file for removal of the condition. For another exmaple, if you have a 10-year card that is expiring, and since obtaining residence you have been convicted of an offense that renders you removable, then filing the I-90 to replace your green card will trigger the discovery of that offense by the government, because you will be fingerprinted as part of the I-90 process. If either of these circumstances may apply to you, you should consult with an immigration attorney immediately.
This is general information only. It is not intended as a substitute for legal advice, and does not create an attorney-client relationship.