President Aleksander Kwasniewski said the planned October date was "not realistic" after the double rejection in France and the Netherlands three weeks ago.
Last week, EU leaders decided to delay ratification of the constitution to allow voters to have time to "reflect." Six countries that planned to hold referendums, including Britain, Denmark and Portugal, have since postponed their votes, with only Luxembourg and Estonia bucking the trend.
On Monday, Polish Prime Minister Marek Belka suggested the parliament -- rather than the electorate --should ratify the constitution given the difficulties persuading voters of its relevance after the French and Dutch rejections.
Celebrity Families of 2014 [PHOTOS]