* Judiciary Committee opens amendment marathon
* Republicans express skepticism and promise long process
* House negotiators still face unresolved issues (New throughout, adds details on amendments and voting)
By Richard Cowan and Thomas Ferraro
WASHINGTON, May 9 (Reuters) - A landmark bill backed by U.S. President Barack Obama to overhaul the nation's immigration system survived unscathed on Thursday during the first day of consideration by a divided Senate Judiciary Committee.
On bipartisan votes, the panel rejected conservatives' attempts to thwart implementation of a centerpiece of the bill - a pathway to U.S. citizenship for millions of undocumented immigrants.
By day's end leading Democratic and Republican senators said the committee had improved the bill.
The panel, composed of 10 Democrats and eight Republicans, accepted 21 relatively modest amendments that focus largely on border security and increased congressional oversight. All but one amendment were agreed to on bipartisan votes.
Eleven other amendments were rejected or withdrawn, many of them Republican bids to bolster border security in ways that went far beyond the steps spelled out in the bill, while also delaying or even killing proposals to legalize undocumented immigrants.
"It is a better bill now than it was this morning," said Republican Senator Jeff Flake of Arizona, a member of the committee and the Gang of Eight senators who wrote the measure.
Democratic Senator Charles Schumer of New York, another committee and Gang of Eight member agreed, hailing the amendments as "good-faith improvements...that make our proposal stronger."
As currently written, the bill would boost funding for border security, revamp visa programs to allow for more high- and low-skilled workers and chart a 13-year path to citizenship for most of the 11 million illegal immigrants in the country.
The committee is expected to complete work on the bill by the end of this month, sending it to the full Senate to face a tougher test. That debate could extend through June or longer.
Backers will need the support of at least 60 of the chamber's 100 members to clear what are expected to be Republican-led procedural roadblocks.
Although the Republican Party has urged its members to embrace comprehensive immigration reform as a way to reach out to the growing number of Hispanic voters, a number of Republicans have resisted.
This, despite Hispanics rebuking Republican candidates in last November's elections, including presidential nominee Mitt Romney, with 71 percent of them voting to re-elect Obama.
Many Republicans favor an incremental approach, one that would focus more on strengthening the 1,969-mile (3,170-km) U.S.-Mexican border. They want to do so without a pathway to citizenship, which critics denounce as "amnesty", for those who entered the United States illegally or overstayed visas.
Throughout the day, two Republican co-sponsors of the bill, Flake and Lindsey Graham of South Carolina, joined with Democrats on critical issues to protect the legalization provision from being derailed.
The voting pattern left the most conservative members predicting the eventual demise of the legislation.
"The committee has voted down every serious border security amendment today," said Texas Republican Senator Ted Cruz. "If it doesn't have real border security, it will not pass (Congress)."
Schumer angrily rejected Cruz's characterization, saying, "It's tough as nails."
In roughly eight hours, the committee plowed through about 30 of the 300 amendments submitted.
Some of the amendments are designed to appeal to the Democratic majority, as well as many Republicans, as ways to improve the measure, which would be the first comprehensive change to immigration laws since 1986.
Others are seen as possible ways to kill it. Four of the "Gang of Eight" senators who crafted the complex measure are on the committee, and those two Democrats and two Republicans have agreed to jointly oppose any amendment seen as a "poison pill."
AVOIDING 'MISTAKES OF THE PAST'
The day began with a warning from the panel's top Republican that he would make the process as long and "arduous" as possible.
"I plan to ask many questions throughout this process," Iowa Senator Charles Grassley warned. "I want to know how the bill doesn't repeat the mistakes of the past."
Grassley, in a statement, promised an "arduous" and "robust" debate.
Grassley followed up with an amendment to require that the Obama administration achieve full control of illegal immigration at every part of the U.S. border before any undocumented people now in the United States could be considered for legal status.
"This amendment would set a standard that would basically delay probably forever" the legalization of the 11 million, Schumer said.
The committee defeated a move by Cruz to delay legalizing illegal immigrants until 40,000 more border patrol agents were hired to join the 21,000 already there. Opponents said that would cost as much as $40 billion and take 10 years to achieve.
POLL BACKS IMMIGRATION POLICY OVERHAUL
The kickoff of Senate Judiciary Committee debate on the bill came as a new Pew Research Center poll found 75 percent of Americans believed immigration policy needed major changes and 73 percent said there should be a way for illegal immigrants to stay in the United States.
But less than half, 44 percent, said they favored allowing illegal residents to apply for citizenship.
During a break, Schumer told reporters he worried "all the time" about a Democratic amendment that Judiciary Committee Chairman Patrick Leahy has offered that would cover same-sex couples in the bill's new immigration reform policies. He said the Gang of Eight was evenly split over that amendment.
It was not yet clear whether Leahy will try to attach that amendment to the bill during the committee's work on the bill or possibly wait until the bill reaches the full Senate.
The panel is to resume work on Tuesday.
Negotiations on a bill in the more conservative Republican-led House of Representatives slogged on.
According to one House source familiar with the negotiations, disagreements remained over several important matters, including how many low-skilled workers should be allowed into the United States for jobs ranging from cooks and hotel maids to construction workers. (Editing by Fred Barbash, Jackie Frank, Peter Cooney and Bob Burgdorfer)