The bipartisan group has dispatched its most prominent conservative, Sen. Marco Rubio, R-Fla., to assuage concerns from the political right about the bill's two most sensitive elements, the path to citizenship, and the border security provisions.
"I think the biggest challenge, and what will ultimately decide this issue, is convincing conservatives that real border security is going to be a part of any package and that there are strong accountability measures and enforcement mechanisms," said Tim Baker, a Florida-based GOP strategist.
The Senate proposal would eliminate a current provision that requires people to file for asylum protection within one year of arriving in the United States. Advocates of the change have argued that the provision is unnecessarily restrictive because many asylum-seekers are not in a position to file cumbersome paperwork in English so soon after entering the country, usually after fleeing a dangerous situation.
Advocates said it is rare for asylum seekers to come from Chechnya, despite the longtime struggle among militants there against Russian control of the region. In the late 1990s, Chechens were the No. 1 migrant group in Europe, but the numbers have never been large for the United States, said Kathleen Newland, co-founder of the Migration Policy Institute.
Most asylum-seekers from the former Soviet Union have been evangelical Christians or Jews fleeing religious persecution, experts said. The Tsarnaev brothers are reportedly Muslim.