"I think as a country we need to do something," Webster said in an interview, echoing the rhetoric of Florida Sen. Marco Rubio and other prominent Republicans. "Doing nothing is amnesty."
The small but growing band of Republicans is trying to strike a balance between conservative activists who want border security and immigration advocates who want a path to citizenship.
Many come from swing districts with sizable Hispanic populations that could make a difference in next year's elections, tipping the balance of power in the GOP-controlled House. The lawmakers also feel the pressure from business interests that rely on immigrant labor.
At the same time, conservative taxpayer groups who typically fund GOP primary challenges have remained largely silent on immigration. Anti-immigration activists have failed to organize large-scale demonstrations or generate the kind of public backlash that killed Congress' last attempt to remake immigration policy, in 2007.
Immigrant advocates, on the other hand, have waged a well-funded, aggressive campaign to push for the legislation.
"Congresspeople who may have been on the fence are realizing it's safe to get in the water," said Ana Navarro, a GOP strategist who led Hispanic outreach for Sen. John McCain's presidential campaign in 2008. "There is safety in numbers."
Some Republicans seem to have little choice.
US Rep. Mike Coffman of Colorado won election in 2008 in a conservative district by campaigning against an immigration overhaul. But an unfavorable redrawing of his district after the 2010 census left him in Democratic-leaning territory that President Barack Obama won last year and where Hispanics make up nearly 20 percent of the population. He is now pushing for a "compassionate" approach to immigration.
US Rep. Joe Heck of Nevada also has seen the Hispanic population grow in his swing district in suburban Las Vegas. Heck has said the path to citizenship outlined in bipartisan legislation passed by the Senate is "reasonable." The state GOP gave him political cover by becoming the first in the country to endorse comprehensiveimmigration changes.