About 11.7 million immigrants are living in the United States illegally, a population that has not varied much over the last three years but may recently be increasing again, according to new estimates published Monday by the Pew Research Center Hispanic Trends Project.

As lawmakers in Washington debate an immigration overhaul that could include a pathway to legal status or citizenship for millions of unauthorized immigrants, the figures from the nonpartisan Pew Center are regarded by many demographers as the most reliable estimates of the number of people who might be eligible for those programs.

The new estimates, which are based on the most recent census data and other official statistics, show that the population of immigrants here illegally did not decline significantly from 2009 to 2012, despite record numbers of about 400,000 deportations each year and stepped-up border enforcement by the Obama administration as well as laws to crack down on illegal immigration in states like Alabama, Arizona and Georgia.

Recent figures, including reports from the Border Patrol of illegal crossings at the southwest border, suggest that the numbers began to grow again last year. But Pew researchers said the increases in the 2012 census data — the latest available — were too small for them to conclusively confirm the recent rise.