By Steve Holland

CRAWFORD, Texas, May 19 (Reuters) - U.S. President George W. Bush on Saturday acknowledged lawmakers' doubts about a U.S. immigration proposal but argued it will help resolve the status of 12 million illegal immigrants in the United States.

With the proposal taking fire from both Republicans and Democrats, the Senate is to begin debate on immigration next week.

Bush used his weekly radio address to open what is likely to be an intense effort to persuade Americans to support the plan as the answer to long-simmering U.S. immigration problems.

"It will help us resolve the status of millions of illegal immigrants who are here already, without animosity and without amnesty," said Bush, who is spending the weekend at his Texas ranch.

The president, in need of a victory to brighten a second term dominated by the chaos in Iraq, wants to resolve the immigration battle before it gets swept up by the presidential campaign to replace him in 2008.

The immigration deal was reached on Thursday between U.S. senators and backed by both Bush and Democratic Senate Majority Leader Harry Reid of Nevada.

The legislation will have to be navigated through some perilous shoals if it is to become law.

Conservative Republicans fear it would lead to an amnesty for illegal immigrants who they say are already weighing heavily on America's social fabric.

At the same time, many Democrats think the elements of the worker program are too tough on immigrants. Labor unions fear the deal will drive down wages.

"I realize that many hold strong convictions on this issue, and reaching an agreement was not easy," said Bush.

The Republican president sought to reassure conservatives who stymied an immigration push last year by fighting for tougher border security measures.

He said the immigration proposal would require that strong border security and enforcement benchmarks - such as doubling the number of Border Patrol agents on the U.S.-Mexico border -- are met before the temporary worker program and other pieces of the legislation would be implemented.

In another move aimed at conservatives, the White House circulated a "Myth/Fact" document seeking to answer critics who contend the agreement amounts to a reward for the thousands who sneaked into the United States.

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