Cantor also said Republicans need to do a better job building public support for some of their ideas.

"[I]f we successfully make the case publicly, bills that could reach the president’s desk include: expanded work requirements for welfare programs, expanded domestic energy production and repeal of IPAB," Cantor wrote.

IPAB is the Independent Payment Advisory Board, which was created to help find Medicare savings but has come under attack from Republicans as a body that would make recommendations that don't have to be approved by Congress.

Other proposals Cantor outlined are bills to reform immigration rules to let people who want to start a business in the United States stay in the country; consolidate the 47 federal job training programs; and give parents "greater control over the education of their children." He also suggested streamlining regulations related to capital investments and medical research and undertaking efforts to boost scientific research.

But Cantor said the details of these proposals would have to be worked out during the Republican retreat early next year.

"When we gather at our retreat in January, our conference will need to further refine and agree upon this list of priorities," he wrote.

Cantor stressed that while Republicans "did not get the partner in the White House that we desired," the two parties must work together to get results in the next Congress. He said that means neither side can expect to get everything it wants.

Still, he indicated that the only way to deal with the fiscal cliff is through fundamental tax reform next year.

"If the president is serious about getting Americans back to work and avoiding a $400 billion tax hike on Jan. 1, he will join us in locking in a process for fundamental tax reform in 2013," he wrote. He added that entitlement reform is also needed.

"The American people will not accept and we will not support the plan of some in the president's party to simply raise taxes to fund failing programs they refuse to reform."