In anticipation of President Barack Obama’s speech Tuesday in Las Vegas to chart a legislative course for an immigration overhaul, lawmakers from both parties agreed on the Sunday morning talk shows that after years of false starts, this might be the year that a broad law gets enacted.

Sens. John McCain, R-Ariz., and Robert Menendez, D-N.J., told Martha Raddatz, filling in for George Stephanopoulos on ABC’s “This Week,” that they are “optimistic.”

For one thing, it has become an issue that Republicans as well as Democrats now want to get behind.

“There is a new appreciation on both sides of the aisle, maybe more importantly on the Republican [side], that we have to enact a comprehensive immigration reform bill,” McCain said. “I see some glimmer of bipartisanship out there.”

McCain, who has been working on various immigration overhaul attempts over the years, told Raddatz that while he was focused on increasing pathways to citizenship, he remained concerned about border security, particularly in his home state of Arizona.

Menendez, after McCain’s comments, agreed that there was reason to be “cautiously optimistic.”

“I see the right spirit,” he said. “I see things that were once on the table … now [back] on the table.”

McCain and Menendez are leading immigration overhaul efforts in their chamber alongside Sens. Charles E. Schumer, D-N.Y., Lindsey Graham, R-S.C., Marco Rubio, R-Fla., and Richard J. Durbin, D-Ill. The bipartisan group of senators is expected this week to release a “set of principles” that would be the foundation for any bill the chamber could consider in the months ahead.

Durbin, the second-ranking Senate Democratic leader, told host Chris Wallace on “Fox News Sunday” that the group would offer a path toward citizenship for illegal immigrants currently in the country, as well as the DREAM Act to help students who lack citizenship and measures to help reunify families.

“We are committed to a comprehensive approach to finally, in this country, have an immigration law we can live with,” Durbin said.

On CNN’s “State of the Union,” Sen. Dianne Feinstein told Candy Crowley that while she was primarily focused on pushing legislation to reinstate the federal ban on assault weapons, she was also playing a role in preparing an immigration policy overhaul bill.

The California Democrat said she would be focusing on agriculture and farm programs, many of which rely on migrant workers to perform seasonal jobs.

During Sunday’s “This Week” show, Republican Rep. David Schweikert of Arizona emphasized the importance of strengthening border security, adding that it was imperative to address drug trafficking across the borders of his state. “People in my district live in fear,” he said.

In an interview with David Gregory on “Meet the Press,” Wisconsin Rep. Paul D. Ryan described the immigration system as one that is “broken [and] needs fixing.”

The 2012 GOP vice presidential candidate also said he believed an immigration policy overhaul was something that could be accomplished this year, adding that he liked principles put forward by Rubio, though he did not elaborate on that comment.

He cautioned that any overhaul’s success would hinge on Obama’s ability to lead: “The president has a big speech coming up, and the question Republicans and Democrats are asking is, ‘Is he looking to play politics or does he want to solve the problem?’”