(CBS News) When President Lyndon B. Johnson signed the 1964 Civil Rights Act into law, he helped put an end to the United States' shameful Jim Crow laws. Five decades later, the struggle for equality and justice continues on several fronts. Four of the five living U.S. presidents and several civil rights leaders are gathering at the LBJ Presidential Library in Austin, Texas this week to commemorate the Civil Rights Act's 50th anniversary and consider its legacy in ongoing debates over issues like immigration reform and gay rights.
The Civil Rights Summit opened on Tuesday with a keynote address from former President Jimmy Carter, as well as panels of lawmakers, attorneys and activists. The speakers Tuesday stressed that civil rights issues transcend partisanship.
Speaking at the Civil Rights Summit in Austin, Texas, former President Jimmy Carter says we've come a long way since his childhood days in a small Georgia town, but there's still further to go.
"As a party we've got to be alert to the fact that this is not and should not be" a partisan issue, Democratic attorney David Boies said. "Lyndon Johnson succeeded because he made clear it was not a partisan issue."
On Wednesday, President Bill Clinton will speak at the event, and civil rights greats like Rep. John Lewis, D-Ga., and basketball legend Bill Russell will participate in panel discussions. On Thursday, President Obama and former President George W. Bush will address the summit.
The clearest connection to the 1960s movement is the ongoing struggle to ensure voting rights.
Another landmark piece of legislation from that era, the Voting Rights Act of 1965, was effectively gutted last year by the Supreme Court. Its ruling left the fate of a key portion of the law in the hands of Congress.
The court ruled that Section 4 of the law, which provided the formula for determining which states must have any changes to their voting laws pre-approved by the Justice Department, was outdated and thus unconstitutional. In the wake of that ruling, several states previously covered by the rule passed voter ID laws making it harder to vote.
If Congress wants to restore the Justice Department's broader authority to monitor voting rules, it will have to rewrite Section 4. In January, Rep. Jim Sensenbrenner, R-Wis., joined four Democrats to introduce legislation to do just that. In a USA Today op-ed last month, he explained why the issue is nonpartisan, arguing that the Voting Rights Act can co-exist with voter ID laws.
"As elected officials, our legitimacy depends on free and fair elections," he wrote. "Support for voting rights and voter identification are consistent goals. Only in hyper-partisan Washington can we lose sight of this."
Last month, 160 Democrats sent a letter to Republican House leaders, urging them to move the legislation forward. So far, however, it hasn't gone anywhere.
On the first day of the Civil Rights Summit, participants discussed a newer front on the struggle for equality: gay marriage.
Ted Olson, a Republican who served as President George W. Bush's solicitor general, explained why he and attorney David Boies took the case against California's same-sex marriage ban (called Proposition 8), all the way to the Supreme Court.
"What David and I have been fighting for is for us to eliminate that vestige of discrimination against citizens who are just the same as the rest of us, who have the same aspirations and the same dreams," he said. "The Supreme Court has said we do not tolerate putting classes of our citizens into boxes, into groups in which we deny them equal rights, equal dignity."
Boies noted that since the Supreme Court last year dismissed the Prop. 8 case and struck down the federal Defense of Marriage Act (DOMA), more than 30 federal judges have considered the issue of gay and lesbian rights -- and all of them have ruled marriage is a constitutional right that cannot be deprived based on sexual orientation.
"As a matter of legal principle, there are simply not two arguments," Boies argued. "The due process and equal protection argument under the precedent of the U.S. Supreme Court makes it absolutely clear the state cannot deprive two people of the right of marriage."
More bluntly, he said, "The other side doesn't have an argument -- they have a bumper sticker that says marriage is between a man and a woman."
So far, gay rights issues have been stalled in Congress by Republican opposition -- just three GOP senators support gay marriage, the Atlantic pointed out, and 10 Senate Republicans voted for the Employment Non-Discrimination Act last year. On the other hand, Congress did manage to repeal the military's "don't ask, don't tell" policy in 2010.
"You are seeing the beginnings of legislative recognition on this issue," Boies said. "Legislative recognition almost always is a lagging indicator."
Later at the Civil Rights Summit on Tuesday, San Antonio Mayor Julian Castro, a Democrat, explained why he saw the fight for immigration reform "in the same vein" as the civil rights movement.
"You look at our nation's history, what we see are different groups coming to the United States and when they lived in the United States were seen as 'other' and were treated that way," he said. "When we think about what we classically think about the civil rights movement, that's what it was about -- people who were seen as different."
Former Mississippi Gov. Haley Barbour, a Republican, said it's in the nation's best interest to advance the legal rights of undocumented immigrants.
"I was raised to believe we are a country of immigrants... and we're better for that, we're a better country for that," he said. "My views about immigration policy are just pure and simple, it is in the best interest of America economically and for other reasons that we ...take the 11 million people that are here illegally and give them the opportunity to be here legally."
Barbour also argued that there is no alternative: "We're talking about 11 million people, millions of whom have been here for year and years and years," he said. "Anybody who thinks we're going to send 11 million people back to where they came from -- well, if they'll tell you that, they'll lie to you about other things."
Immigration reform legislation has been stalled in the House, even though Speaker John Boehner, R-Ohio, said as recently as last month that it remains a priority for him. Barbour said it shouldn't be surprising that the GOP wants to take up the issue.
"Both parties necessarily are broad coalitions, and both of them are much broader than... people like to give credit for," he said.
Castro, meanwhile, said that if immigration reform legislation isn't passed this year, he believes it will be before the 2016 election.