In a letter sent to the freshman class, Cantor offered congratulations and said voters delivered a message that they want the two parties "to find common ground on the nation's most pressing issues," The Hill reported Friday.
When he was first elected majority leader in 2011, Cantor changed the House calendar to ensure recesses and vote schedules were more predictable to allow enough time both for district work at home and uninterrupted committee hearings in Washington.
"I strove to deliver a predictable schedule that accommodated time spent with constituents at home and substantive committee work here in Washington," Cantor wrote to the new members. "I am finalizing the 2013 calendar and welcome any input you may have now, or in the future."
A Cantor aide told The Hill the House likely would adhere to its two weeks on, one week off schedule.