Washington ( CNN ) -- A compromise amendment intended to ease congressional passage of sweeping immigration legislation easily won Senate approval Wednesday . The 69-29 vote set up a procedural motion immediately afterward to limit debate on the roughly 1,200-page bill , which would provide an eventual path to citizenship for millions of immigrants living illegally in the country . While some further amendments still could be considered , the measure appeared headed to a final Senate vote by the end of the week after the procedural motion passed in a 67-31 vote . Backers of the bill want the Democratic-led Senate to pass it with a solid majority to demonstrate growing bipartisan momentum as the measure heads to the GOP-controlled House of Representatives . The compromise amendment by Republicans John Hoeven of North Dakota and Bob Corker of Tennessee would increase border security , a demand by conservative opponents of the immigration bill . Justices could put an end to hard choice for gay couples . `` I hope our colleagues in the House of Representatives will follow the Senate 's lead , and work to pass bipartisan reform that both Democrats and Republicans can support , '' Senate Majority Leader Harry Reid , D-Nevada , said before Wednesday 's votes . Conservative GOP Sen. Chuck Grassley of Iowa , an opponent of the Senate bill , conceded it s likely to pass and called on House Republicans to make things right . `` I expect the House of Representatives to fix this miserable failure , '' Grassley said . Republican leaders say the House will consider the issue in several smaller proposals instead of a comprehensive single measure , a process that would allow more debate and votes on specific provisions . Earlier Wednesday , House Speaker John Boehner reiterated to GOP members that he opposes having the House take up any Senate immigration legislation , according to Rep. John Fleming . Fleming , a Louisiana Republican , said Boehner told the weekly policy meeting that the House would work on its own immigration bills . If enacted , the bill would create a path to citizenship for roughly 11 million undocumented immigrants while enhancing security along the border with Mexico . Among other things , the compromise border security amendment would add 20,000 border agents , complete 700 miles of fence along the boundary with Mexico , and deploy $ 3.2 billion in technology upgrades similar to equipment used by U.S. forces in Iraq and Afghanistan . Opinion : Protect rights of immigrant whistle-blowers . The proposal also includes stronger worker eligibility verification standards and border entry-exit controls . Most undocumented immigrants would be eligible for permanent residency only after those five conditions have been met and verified by the Department of Homeland Security . Hoeven and Corker introduced the compromise amendment last week , saying it incorporated proposals from other senators to try to fix a broken immigration system . Grassley and other opponents argued the legislation amounts to an amnesty for immigrants who broke the law by living illegally in America . They argued the promises of increased border security before giving undocumented immigrants permanent residency would end up proving empty . `` It does nothing to change the legalization-first philosophy and does little more than offer false promises that the American people can no longer tolerate , '' Grassley said . If eventually passed into law and signed by President Barack Obama , the bill would be the first major immigration reform since 1986 , during the second Reagan administration . Grassley conceded he voted for the 1986 measure , which also called for increased border security , and called his support then a mistake he regrets . Farm bill failure portends problems for immigration in the House . The 2013 version was drafted by a Senate `` Gang of Eight '' composed of four Democrats and four Republicans motivated by political and policy needs . Both parties concede the nation 's immigration system is broken , and some Republicans believe that GOP refusal to work with Democrats on the matter would mean a repeat of the 2012 presidential election in which Obama won a strong majority of the Hispanic vote . However , other Republicans fear that providing a path to legal status for millions of undocumented immigrants would bolster support for Democrats from the new voters . Florida Sen. Marco Rubio , the most prominent Republican in the `` Gang of Eight , '' told CNN 's Dana Bash last week that he understands `` why conservatives are upset . '' `` They 've seen all these promises in the past that have n't been delivered , '' Rubio said . But the status quo on immigration `` is hurting America , '' he added . `` And if nothing passes , then this disaster that we have now , that 's what 's going to stay in place . '' Opinion : Why cops should back immigration reform . CNN 's Alan Silverleib , Ted Barrett and Deirdre Walsh contributed to this report .
NEW : A separate vote limits further debate , setting up a final vote as soon as Thursday . Comment: A final vote on the immigration bill could occur by the end of the week . It would increase border security and provide an eventual path to citizenship for millions .