Story Highlights • NEW: House Republican caucus passes resolution opposing bill
• NEW: Debate on two dozen amendments to commence Wednesday
• 64 senators vote to bring immigration bill back for consideration
• Bush dispatches Commerce, Homeland Security heads to work out compromise
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WASHINGTON (CNN) -- Though the Senate voted Tuesday to bring President Bush's immigration reform bill back to the Senate floor, objections to any of two dozen amendments to be debated starting Wednesday could kill the bill for the year.
And even as the Senate moved forward, House Republicans late Tuesday voted overwhelmingly in favor of a resolution opposing the immigration bill -- a move that could place a significant roadblock in front of the measure even if it clears the Senate.
By a vote of 114-23, the House Republican Conference approved a statement by Rep. Pete Hoekstra of Michigan that simply read: "Resolved: The House GOP Conference disapproves of the Senate immigration bill." The vote came during a closed-door meeting.
The lack of Republican support could doom the immigration bill because House Democratic leaders have previously said they would not bring it to the House floor unless at least 70 of the 201 GOP members were on board.
House Minority Leader John Boehner, R-Ohio, said, "It's clear that there is a large number of House Republicans who have serious concerns with the Senate bill."
Earlier in the Senate, proponents of the bill received four more than the 60 votes necessary to send the legislation to the floor for debate after several pleas from Bush over the last two weeks, including a rare trip to Capitol Hill to twist a few arms and a final speech Tuesday morning.
"I view this as a historic opportunity for Congress to act," Bush told an audience of supporters at the Eisenhower office building. "This is a moment for people who have been elected to come together, focus on a problem and show the American people we can fix a problem."
The bill includes $4.4 billion for border protection, work-site enforcement and tamper-proof ID cards; sets up a temporary worker program to address the needs of employers who rely on migrants; and requires that migrants learn English. It also offers a path to citizenship to the estimated 12 million people in the United States illegally.
One of the bill's architects, Sen. Edward Kennedy, D-Massachusetts, called Tuesday's vote "a major step forward for our national security, for our economy, and for our humanity."
"We did the right thing today because we know the American people sent us here to act on our most urgent problems. We know they will not stand for small political factions getting in the way," Kennedy said in a statement.
A similar test vote earlier this month received only 45 votes, and only nine of them from Republicans. On Tuesday, 24 Republicans joined 39 Democrats and independent Sen. Joseph Lieberman to proceed with debate.
Bush said that Commerce Secretary Carlos Gutierrez and Homeland Security Secretary Michael Chertoff will work with senators to reach a compromise.
"We are certainly pleased with the early vote on the motion to proceed," White House spokesman Tony Snow told reporters shortly after the Senate decision. He said he looks forward to the debates.
Opponents of the bill say that the path to citizenship amounts to amnesty for those who entered the country illegally. The 24 amendments to be considered -- 12 for Democrats and 12 for Republicans, seek to change some of the more controversial parts of the legislation.
Sen. John Cornyn, R-Texas, one of the bill's more vocal opponents said he is still concerned about enforcing tougher laws.
"My concern is the gulf between the promise being made to the American people and the likelihood that the promise will be carried out," Cornyn said before the vote. "The White House said this is of no concern because they will declare them ineligible and deport them.
"The question Americans are asking is, 'Will they? Can they,' " Cornyn said.
Senate Majority Leader Harry Reid, D-Nevada, said the Senate had to address the issue.
"The stakes are too high for inaction," Reid said. "We are the Senate of the United States. People said, 'The issue is too complex, let's not do it.' We have to take hard votes.
"Mr. President, we have an immigration system that is broken and needs to be fixed. That's what we're trying to do is fix this," Reid said.
A CNN/Opinion Research Corporation poll released Monday showed 47 percent of Americans opposed the bill, while 30 percent supported it and 19 percent said they didn't know enough about it to make a judgment. The poll's sampling error was plus or minus 3 percentage points.
However, the poll found a significant division among opponents of the immigration plan. About 28 percent said they were opposed because it did too much to help illegal immigrants, but 15 percent said they were opposed because it did too little.
So while much of the opposition to the bill has come from those who believe it is too soft on illegal immigration, the poll found that 45 percent of Americans either support the bill or want it to be more immigrant-friendly, compared to 28 percent who feel it's already too immigrant-friendly.
CNN's Dana Bash and Evan Glass contributed to this report.
President George W. Bush.
The discussion on the , which, if passed, would result in a temporary worker program, was put back on the political agenda. The  voted 64–35, which, though not sufficient to pass the bill, was enough to resume debate on the subject.

President Bush has been working to get the bill back into the agenda, making a trip to  to "twist a few arms" according to . He also gave a speech on the subject on Tuesday morning. 

The bill faces stiff opposition from Republicans in Congress, who say that "it would do little to stem the flow of illegal immigration into the United States."

President Bush spoke about the issue, saying that, "I view this as a historic opportunity for Congress to act... This is a moment for people who have been elected to come together, focus on a problem and show the American people we can fix a problem."