The statements of support come after an intense campaign by pro-immigration advocates, who targeted House of Representative members at town hall events prior to rallies, drives and other events across the country.
With Webster of Florida and Schock of Illinois, 21 House Republicans now support the measure, ABC News reported.
"We would much prefer a big comprehensive bill, but any way that the House can get there is OK by us," the New York Democrat told CNN. "I actually am optimistic that we will get this done."
Schumer, a leader of the bipartisan "Gang of Eight" senators whose comprehensive immigration-reform legislation passed the Senate in June, said he'd "had a lot of discussions with various members of both parties in the House. Things are moving in the right direction.
"The initial reaction was the House isn't going to take up any bill," Schumer added. "That would have been very bad -- no bill. Now, they're doing it in pieces. A couple of their pieces are very similar to our bill."
House Speaker John Boehner, R-Ohio, has said the House would not consider the Gang of Eight bill, which he has called "flawed legislation rushed through the Senate." He said the lower chamber would instead consider immigration in smaller, "bite-sized" pieces over the coming months.
Schumer told CNN Wednesday he wasn't concerned by that, explaining if the House passes a number of smaller immigration bills, "they'll all get agglomerated as we go to conference at some point."
He said he would not dictate to the House what it should do, but "there are certain bottom lines for us: We do need some kind of path to citizenship. We do need to reform the broken system. But that's the issue here. Everyone -- except a small few on the hard right who want to do nothing -- know the system is broken."
A path to citizenship for 11 million immigrants in the United States illegally is the most controversial provision of immigration reform among many House Republicans.
But House Judiciary Committee Chairman Bob Goodlatte, R-Va., has floated an idea he says would rely partly on existing law to let many immigrants living illegally in the country gain citizenship.
People in both parties told The Wall Street Journal the idea has the potential to win backing from at least some Republican House members who don't want immigrants in the country illegally to get special treatment unavailable to other foreigners.
Goodlatte's idea would have Congress grant the immigrants a provisional legal status, like the Senate passed. But then the immigrants would use existing laws that let foreigners legally in the country seek green cards, or permanent legal residency.
This could then be followed by citizenship in already available ways -- marrying a U.S. citizen, having a U.S. citizen relative petition for them or having a U.S. employer sponsor their application.
"All of those are ways they could then eventually find themselves permanent residents and, ultimately, citizens, but none of those would be special ways that have been made available only to people who have come here illegally," Goodlatte told C-SPAN's "Newsmakers" program last month in one of several public appearances in which he has described his evolving idea.
No immigrant living in the country illegally would gain legal status before efforts are in place to secure the border with Mexico and tighten immigration law enforcement, Goodlatte has said.
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