Among the plan’s new proposals is the creation of a commission of governors, law enforcement officials and community leaders from border states that would assess when border security measures had been completed. A proposal would also require that an exit system be in place for tracking departures of foreigners who entered the country through airports or seaports, before any illegal immigrants could start on a path to citizenship.

The lawmakers intend for their proposals to frame the debate in the Senate, which is expected to take up immigration this spring, ahead of the House of Representatives. Compared with an immigration blueprint from 2011 that White House officials have said is the basis for the president’s position, the senators’ proposals appear to include tougher enforcement and a less direct path for illegal immigrants than Mr. Obama is considering.

In a parallel effort, a separate group of four senators will introduce a bill this week dealing with another thorny issue that is likely to be addressed in a comprehensive measure: visas for legal immigrants with advanced skills in technology and science. The bill, written primarily by Senator Orrin G. Hatch of Utah, a Republican, and Senator Amy Klobuchar of Minnesota, a Democrat, would nearly double the number of temporary visas, known as an H-1B, available each year to highly skilled immigrants. It would also free up more permanent resident visas, known as green cards, so those immigrants could eventually settle in the United States and go on to become citizens.

In a sign of the rapidly changing mood in Washington on immigration, the two groups of senators and the White House have been vying in recent days to see who would unveil their proposals first.

Senator Robert Menendez of New Jersey, a Democrat who was one of those negotiating the comprehensive principles, said the senators finally agreed that any legislation should include a pathway to citizenship.

“First of all, Americans support it, in poll after poll,” said Mr. Menendez, who was interviewed along with Mr. McCain by Martha Raddatz on Sunday. “Secondly, Latino voters expect it. Thirdly, Democrats want it. And fourth, Republicans need it.”