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. 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. "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.