By Susan Heavey WASHINGTON (Reuters) - House of Representatives Speaker John Boehner said he expects an overhaul of immigration rules to become law by the end of the year, but that the Senate's version "doesn't go far enough" to secure the U.S. border with Mexico or enforce the proposed new system.

By Caren Bohan WASHINGTON (Reuters) - Senator Rand Paul, a conservative Republican whose vote is being courted by supporters of a broad U.S. immigration bill, said on Sunday he is open to voting for the measure but wants changes, including tougher border security requirements. Paul, who has hinted at an interest in running for president in 2016, in March backed the concept of a path to citizenship for undocumented immigrants that is at the heart of a comprehensive immigration bill under consideration in the U.S. Senate.

WASHINGTON - Senate supporters of far-reaching immigration legislation accepted minor changes in public while negotiating over more sweeping alterations in private Monday as they drove toward expected Judiciary Committee approval by mid-week. In a long day of drafting, the panel voted to begin phasing in a requirement for foreigners to undergo fingerprinting when they leave the country. Lawmakers also agreed to make an immigrant's third drunk driving conviction a deportable offence in some cases.

The US Senate has spent months thrashing out a comprehensive immigration reform bill, but House members are now getting in on the action, introducing two smaller measures on the issue as early as Thursday. Representative Bob Goodlatte, chairman of the House Judiciary Committee that will shepherd any immigration legislation through the chamber, said his panel would file "several" standalone bills and suggested he preferred that method to the Senate's sweeping, 844-page bill introduced last week.