''I'd like to see more prolife Democrats," Heft said, ''and social justice Republicans."
Immigration is not the first issue to split Republican and Catholic leaders.
Pope John Paul II opposed the US war on Iraq and the death penalty, for example.
But the latest differences have emerged only months before much of the Congress, which is now controlled by the Republicans is up for reelection.
The rifts also have arisen as the Republicans and Catholics had seemed closer than ever.
''Right now, a higher proportion of Catholic voters would identify with the Republican Party, or some of the themes that the Republican candidates have been using," said David Leege, a professor emeritus at the University of Notre Dame and a specialist on Catholics and politics.
But the impact of the immigration debate is unclear.
''The jury is out on the Catholic vote in long run," Leege said.
Catholics, who had once been perceived as solidly Democratic, have been moving toward the Republican Party for the past 25 years or so.
When Catholics established themselves financially, they started voting less according to religious ties and more according to economic interests.
The Democrats' support of abortion rights also drew them to GOP candidates.
President Bush, a Methodist, won the 2004 Catholic vote 52 percent to 47 percent over the Democratic nominee, John F. Kerry, who is a Roman Catholic.
Leading to the election, bishops had warned Catholic legislators that they risk ''cooperating in evil" if they vote for candidates supporting abortion rights.
Church leaders insisted that their position was nonpartisan.
Yet the timing of their statements was a boon to Republicans, since Kerry backs abortion rights.
But now, many of these same bishops are accusing GOP lawmakers of lacking compassion for illegal immigrants.
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