WASHINGTON — As a bipartisan group of eight senators prepared to introduce a plan early next week to overhaul the nation’s immigration laws, Senate negotiators have agreed to a cutoff date that could bar hundreds of thousands of immigrants from the path to legalization provided in the legislation.

Illegal immigrants who arrived in the country after Dec. 31, 2011, could be ineligible to apply for legal status — and potentially citizenship — under the new immigration bill, which will provide a 13-year path to citizenship for the 11 million illegal immigrants already living in the country.

Every bill that legalizes immigrants has a cutoff date for eligibility, to discourage a surge of people who have heard about potential legislation. Immigration advocates and Democrats in the group had been pushing for the date to be as current as possible — Jan. 1, 2013 — while Senator Marco Rubio, Republican of Florida and a member of the group, originally argued for 2008.

The Dec. 31, 2011, deadline represented a compromise, as well as something of a victory for Mr. Rubio.