Agreement over a highly touted Senate compromise on illegal immigration fell apart Friday as Democrats, Republicans and the White House pointed fingers over who was to blame for the present impasse over the bill.

Senators said their work on the controversial issue would now be postponed until after Congress returns from the two-week recess, when the bill is expected to be taken up again by the Senate Judiciary Committee.

"We're intent ... on moving forward," Sen. John McCain, R-Ariz., told reporters after the vote, adding that although the process had broken down Thursday night, he was "confident" a bill would eventually emerge from the Senate.

"I think politics got in front of policy in this issue," added Sen. Edward Kennedy, D-Mass.

It's not clear when the bill would be taken up by the full Senate, but Senate Judiciary Committee Chairman Arlen Specter, R-Pa., said Friday he hoped that could happen by early May.

The compromise reached Thursday — which was then stalled on Friday — sought to divvy the estimated 11 million or so illegal immigrants into three groups: those who have been inside the country for more than five years who would have the best chances to gain citizenship; those who have been in the country for between two and five years and would face more obstacles in gaining citizenship, but could remain in the country; and those who have been in the country for fewer than two years who would have to leave and apply for visas before they could return.

The bill also provides a new program for 1.5 million temporary agriculture industry workers over five years. It includes provisions requiring employers to verify they've hired legal workers and calls for a "virtual" fence of surveillance cameras, sensors and other technology to monitor the nearly 2,000-mile U.S.-Mexican border.

On Friday, however, that compromise — named the Hagel-Martinez compromise after its sponsors — received only 38 of the 60 votes that would have brought the bill to cloture and allowed an up-or-down vote on the bill. If the bill had received those 60 votes, it would have been protected from amendments that may have weakened it.

Republicans were united in the 38-60 parliamentary vote, with even GOP supporters of the bill saying that its opponents should get votes on their amendments. Democrats, who have insisted on no amendments, lost six votes from their members.

An alternative bill by Senate Majority Leader Bill Frist — with no provision to let illegal immigrants stay but imposing large fines on employers who hire them — received even less support in a 36-62 test vote. That measure also would have focused more on border security. McCain said the fact that Frist's measure had so little support was a good sign that the Senate was committed to a broader immigration reform.

Frist, R-Tenn., called the collapse of talks on the compromise bill tragic "that we in all likelihood are not going to be able to address a problem that directly affects the American people."

White House spokesman Scott McClellan laid blame directly on Senate Majority Leader Harry Reid of Nevada.

"Unfortunately, the Senate minority leader prevented voices from being heard and amendments from being considered," McClellan said, calling on Reid to stop blocking the process.

Frist said some 400 amendments had been offered on the bill, and Democrats had only allowed three to be voted on.

Specter also blamed the delay on the Democrats.

"It's not gone forward because there's a political advantage for Democrats not to have an immigration bill," Specter said.

He said Democrats perceive a benefit in having only a GOP-written House bill that criminalizes being an illegal immigrant. That bill has prompted massive protests across the country, including a march by 500,000 people in Los Angeles last month. Democrats blamed Republicans for insisting on amendments that would weaken the compromise that Senate leaders in both parties had celebrated Thursday.

Blasting back, Reid said the "Bush Republicans unwilling to support the bipartisan compromise" were "stonewalling efforts to secure the country," and singled out Frist for the problems.

"His position on this matter simply defies logic," Reid said, criticizing the Senate's top Republican for saying he supported the compromise on Thursday, then leading efforts to defeat it Friday.

"This opportunity is slipping through our hands like grains of sand," said Assistant Senate Democratic Leader Dick Durbin of Illinois.

Earlier Friday, President Bush prodded lawmakers to keep trying to reach an agreement.

"An immigration system that forces people into the shadows of our society, or leaves them prey to criminals is a system that needs to be changed," Bush said at the National Catholic Prayer Breakfast. "I'm confident that we can change our immigration system in ways that secures our border, respects the rule of law, and, as importantly, upholds the decency of our country."

According to a recent FOXNews/Opinion Dynamics poll, a clear majority of Americans believe illegal immigration is a very serious problem for the country, although only one in four say they believe it is a serious problem in their community.

Seven in 10 people said they favor allowing illegals who have jobs to apply for temporary worker status, but eight in 10 said they think it is unfair to grant rights to illegal immigrants while others wait to come into the country illegally — what some refer to as amnesty.

The Senate has grappled with immigration reform for several weeks as hundreds of thousands of protesters have taken to the streets and Bush has repeatedly called for fast action on immigration reform. The president favors a so-called guest worker program, which would allow many immigrants who illegally entered the country to gain a legal pathway to citizenship.

Some Republicans have criticized a guest worker proposal as amnesty — giving illegal immigrants an unfair advantage to citizenship over those who have pursued legal avenues.

Bush on Thursday applauded the Senate's work and said, "I would encourage the members to work hard to get the bill done prior to the upcoming break."

The House has passed legislation limited to border security, but Speaker Dennis Hastert, R-Ill., and other leaders have signaled their willingness in recent days to broaden the bill in compromise talks with the Senate.

But Rep. Tom Tancredo, R-Colo., said anything with what he called amnesty would not get agreement from a majority in the House.

Although the Senate was to be in recess for the next two weeks, it was clear that its members would be taking the time to rally support.

And the public was not expected to let the issue get swept under the rug. Demonstrations in support of the compromise were planned for Monday across the nation, including one in Washington that organizers claimed would draw 100,000 people.

The Associated Press contributed to this report.