Sen. Chuck Schumer, D-N.Y., who was part of a bipartisan group that drafted a comprehensive immigration reform bill last June, said Monday that immigration reform still has a chance of passing this year.

He said in an interview on MSNBC that Republicans would like to see an immigration overhaul in Congress, but do not want to vote for it individually, Fox News Latino reports.

"Most people are for immigration reform. Most Republicans, they're in the vote-no, pray-yes caucus, they want it to pass as long as they don't have to vote for it. I still think we have a chance to pass it this year," Sen. Schumer told MSNBC.

The Senate bill includes measures for tightening border security, expanding foreign worker visas and providing a pathway to citizenship for undocumented immigrants. The bill stalled in the House, in which a group of mostly conservative Republicans vowed not to approve the bill due to the measure that would give a pathway to citizenship for undocumented immigrants.

While many House Republicans continue to oppose the bill, Schumer said other Republicans in the House support comprehensive immigration reform.

He also said the summer may be the best time for the bill to move forward in Congress, as Tea Party primaries will have ended.

He added that many Republicans realize that they need to reform the immigration system before the presidential election; the GOP could be blamed for not moving reform forward, he said.

"The leadership of the caucus realizes one thing, they won't do it in 2015, because you have the Republican primaries pulling to the right," Schumer said. "And [not doing it] most certainly means they're going to lose in 2016."

Schumer said former Florida Gov. Jeb Bush and House Speaker John Boehner, R-Ohio, are open to reforming the immigration system in a way that tightens enforcement of laws and border security while also providing a path to legal status.

While Boehner and other Republicans released a set of immigration reform principles earlier this year at the Republican caucus, he then backed away from the issue, claiming that President Obama would not enforce immigration laws.

On Sunday, Bush, who hinted that he may run in 2016, said in an interview with Fox News that those who enter the country illegally do so because they want to provide a better life for their families, and that what they do is "not a felony."

"It's an act of love. It's an act of commitment to your family," Bush said. "I honestly think that that is a different kind of crime. There should be a price paid, but it shouldn't rile people up that people are actually coming to this country to provide for their families."

Schumer said in reference to Bush, "He's showing where people are at...Jeb Bush represents the more positive wing of the Republican Party...We have a good chance of passing it this year. Speaker Boehner wants to do it."