WASHINGTON—Senate Republicans are running into internal resistance to their proposed repeal of the estate tax, making it a potential casualty of the trade-offs the GOP faces in its effort to overhaul the tax code.

The party’s leaders included estate-tax repeal in the tax-overhaul framework they released last week. But Republican Sens. Mike Rounds of South Dakota and Susan Collins of Maine said this week that repeal isn’t needed. Others say their desire to eliminate the tax must be balanced against other priorities including...