WASHINGTON (AP) — The immigration debate is shifting to the Republican-led House, where lawmakers have shown little appetite for the large-scale, comprehensive approach their Senate colleagues embraced last week.

The Republican chairman of the House Judiciary Committee said Sunday that any attempt at comprehensive immigration legislation cannot offer a "special pathway to citizenship" for those in the United States illegally. Democrats have called that position a deal-breaker.

Meanwhile, both parties eyed the politics that could yield electoral victories or irrelevance among the growing Hispanic voting bloc.

Rep. Bob Goodlatte, the Virginia Republican who leads the House Judiciary Committee, said he does not foresee a proposal that could provide a simple mechanism for immigrants here illegally to earn full standing as U.S. citizens. His committee members have been working on bills that address individual concerns but have not written a comprehensive proposal to match the Senate's effort.

A pathway to legal standing, similar to that of immigrants who have green cards, could be an option, he said.

Unacceptable, said Sen. Chuck Schumer, D-N.Y.

"No Democrat will vote for any bill without a path to citizenship," said Schumer, who helped write the Senate immigration plan that passed that chamber last week.

The Senate bill would provide a long and difficult pathway to citizenship for those living in the country illegally, as well as tough measures to secure the border. In the Democratic-controlled Senate, 14 Republicans joined all Democratic senators and independents in the 68-32 vote.

In the Republican-led House, conservatives have stood opposed to any pathway to citizenship for those workers. House lawmakers have urged a piecemeal approach to the thorny issue instead of the Senate's sweeping effort. House Speaker John Boehner has ruled out taking up the Senate bill and said the Republican-controlled chamber would chart its own version of the legislation with a focus on border security.

Illustrating the strong opposition among conservative lawmakers, Rep. Trey Gowdy, R-S.C., said flatly: "The Senate bill is not going to pass."

If immigration falls, so too could the GOP's national prospects.

Sen. John McCain, the 2008 Republican presidential nominee and an author of the current Senate immigration bill, said "Speaker Boehner has a tough job ahead" to convince his caucus to act.

"Republicans realize the implications of the future of the Republican Party in America if we don't get this issue behind us," McCain said.

House Democratic leader Nancy Pelosi similarly predictied electoral doom if Republicans thwart the efforts to address the estimated 11 million immigrants now in the United States illegally. She said Republicans should follow the Senate's lead "if they ever want to win a presidential race."

"We wouldn't even be where we are right now had it not been that 70 percent of Hispanics voted for President Obama, voted Democratic in the last election," Pelosi said. "That caused an epiphany in the Senate, that's for sure. So, all of a sudden now, we have already passed comprehensive immigration reform in the Senate. That's a big victory."

In 2012, Obama won re-election with the backing of 71 percent of Hispanic voters and 73 percent of Asian-American voters. A thwarted immigration overhaul could again push those voting blocs toward the Democrats' side.

If an immigration bill fails, Democrats stood ready to blame Boehner and his party.

"Will he allow a small group, maybe even a majority of his caucus, to control the debate and the future on this issue?" asked Rep. Luis Gutierrez, D-Ill. "If he decides to do that, we will then end in a stalemate and an impasse once again."

Goodlatte and Gutierrez spoke to CNN's "State of the Union." Schumer, Gowdy and McCain were on "Fox News Sunday." Pelosi was on NBC's "Meet the Press."