Rubio is actually a NeoConservative, which you would characterize as being a big government fiscal conservative, a hawk, and a social liberal, which means he is pro-choice, supports homosexual rights, and immigration reform. But, being a presidential candidate, he has to obfuscate his position on social issues, which means he had to abandon the immigration legislation he helped write.
As for immigration reform, what is being proposed today is not much different from 2005 and 2006. Shumer replaced Ted Kennedy and Rubio replaced Mel Martinez.
In 2006 the GOP Senate began by trying to pass CIRA, which was Kennedy-McCain, but they didn't have enough votes for cloture, so the Hegel-Martinez compromise emerged, which the senate passed, after which, the GOP House walked away without acting. Rubio and the Gang of 8 passed their legislation in the Senate and the GOP House refused to take it up.
So the dems won the House and Senate in Nov 2006, which means they controlled the committees, and the attempt in 2007 to pass immigration reformed turned into a battle between the unions and Ted Kennedy, which the unions won, and they killed immigration reform, with the help of 4 republicans.
A conservative who supports big government is a liberal who calls himself conservative
Which is what Rubio is