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NEW YORK, NY - NOVEMBER 12: Immigration reform advocates demonstrate on November 12, 2013 in New York City. Some 100 demonstrators called for Republican U.S. Congressman Michael Grimm, who represents New York City's 11th District, to back comprehensive immigration reform legislation in the House of Representatives. The 11-mile "pilgrimage for the 11 million" undocumented immigrants went from midtown Manhattan to Grimm's Staten Island office and was organized by the New York Immigration Coalition. (Photo by John Moore/Getty Images) John Moore, Getty Images

House GOP leaders unveiled their broad immigration principles last week that gave hope to advocates and the Obama administration that the first changes in the nation's laws in three decades might happen in the coming months.

Immigration legislation is one of the top priorities for Obama's second term.

But several of the conservatives were adamant that the House should do nothing on the issue this year, a midterm election year when the GOP is angling to gain six seats in the Senate and seize majority control. Democrats currently have a 55-45 advantage but are defending more seats, including ones in Republican-leaning states.

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A new immigration reform proposal from the House Republican leadership has triggered an intramural fight inside the party. Jeff Pegues reports.

Labrador's comments were noteworthy as he was one of eight House members working on bipartisan immigration legislation last year. He later abandoned the negotiations.

"This is not an issue that's ready for prime time to move legislatively," said Rep. Joe Barton, R-Texas, who said Republicans should use the principles to begin a dialogue with Hispanics.

Rep. Jim Jordan, R-Ohio, said the House should focus on the four bills dealing with security that the Judiciary Committee approved last summer. Absent any action on those bills, Jordan said it would be tough to do any immigration legislation this year.

The definitive statements from the conservatives came as Douglas Elmendorf, the head of the Congressional Budget Office, told a House panel that the comprehensive, Senate-passed immigration bill would have a positive impact on the nation's finances.

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House conservatives: No immigration reform in 2014