As a Republican-led effort to bring more high-skilled foreigners into the country is gaining momentum on Capitol Hill, a GOP rift threatens the proposal as much or more than White House opposition.

Senate Finance Committee Chairman Orrin Hatch, R-Utah, introduced legislation this month that would tweak the nation’s immigration laws, making it easier for high-tech firms in the United States to hire more foreign specialists in so-called “STEM” fields — science, technology, engineering and math.