Powered by the results of the November elections, a bipartisan group of top senators on Monday floated the latest proposal to overhaul the nation’s shattered immigration system — but acknowledged they are at the earliest stages of what is a fragile balancing act.

Led by Sen. John McCain, Arizona Republican, and Sen. Charles E. Schumer, New York Democrat, the eight lawmakers said they want to give all illegal immigrants instant legal status, to expand pathways for legal immigration and to enact more border security.

The framework is close to the 2007 bill that collapsed after voters shut down the chamber’s switchboard with angry phone calls and 53 senators, including 15 Democrats and one independent, joined a filibuster.