US immigration reform set for first votes in Senate 11 June 2013 Last updated at 01:44 The US Senate is set to hold the first votes on immigration reform, starting a multi-week fight to finalise the bill. The two procedural votes on Tuesday are expected to pass as some senators who oppose the bill or certain elements of it say debate should move forward. At the core of the legislation is a 13-year path to citizenship for immigrants who came to the US illegally. The bill enjoys bipartisan support, but one of its authors says the legislation needs stricter border control measures. Florida Senator Marco Rubio says he supports an amendment by fellow Republican Senator John Cornyn requiring additional border security before any immigrant can obtain permanent residence, commonly known as a green card. But Senate Majority Leader Harry Reid, a Democrat, has said Sen Cornyn's amendment is a "poison pill." Thoughtful solution The bill currently includes $6bn (£3.8bn) to strengthen border security, and requires employers to check each employee's legal status. Aside from the path to citizenship, which would begin with a provisional status for an estimated 11 million people, the legislation also creates new or expanded visa programmes for both high-skilled and agricultural workers. The legislation gained another Republican supporter on Sunday when New Hampshire Senator Kelly Ayotte told CBS News it was a "thoughtful bipartisan solution to a tough problem." But some Republicans argue the bill would reward those who broke the law by entering the US illegally. During floor debate on Monday, Iowa Senator Chuck Grassley said the legislation "repeats our past mistakes." Correspondents say many Republicans acknowledge the need to embrace reform, given that Hispanics - an increasingly key voter bloc and a significant percentage of immigrants - overwhelmingly chose Barack Obama in last November's presidential election. Following Tuesday's procedural votes, the Senate will begin to consider a series of amendments to the almost 900-page bill. Sen Cornyn's border security bill will be among those debated, as well as measures on issues including back taxes and healthcare coverage. In the existing bill, only after 10 years and once applicants receive a green card would they be able to qualify for tax breaks while buying medical insurance under President Obama healthcare reform law.