In a moderated discussion before reporters at the Bipartisan Policy Center, a nonprofit research group, both Republicans said they generally supported a bill under debate in the Senate and were guardedly optimistic that overhaul legislation would pass Congress this year.

Their comments highlighted the rift among conservatives over the bill, which includes a pathway to citizenship for 11 million immigrants here illegally. Senator Jeff Sessions of Alabama, a Republican who is a leading opponent of the measure, said this week on the Senate floor that it would bring an influx of foreign workers that “would be disastrous for the wages and job prospects of U.S.