In the wealthy ski towns of Summit County, Colo., where affordable housing is so scarce that some waitresses and ski-lift workers sleep in parking lots, wide-open land is plentiful, as it is across the housing-starved Mountain West.

But much of it is owned by the federal government and off limits for development. And as of Tuesday, it looks like it will stay that way.

Senator Mike Lee, a Utah Republican, had pitched a wholesale auctioning of federal land, in part as a way to build housing, and he planned to include it in President Trump’s far-reaching domestic policy bill.

But it ran into a brick wall of bipartisan opposition even before Monday night, when the Senate’s parliamentarian, who judges what provisions can be included in the bill to avoid a filibuster by Democrats, ruled that much of Mr. Lee’s sell-off proposal would violate the strict Senate rules that Republicans were using to pass the legislation with a simple majority.

Summit County helps show why Mr. Lee’s plan now appears moribund. Even where people are desperate for affordable housing, opposition to selling public lands, potentially for housing, was widespread from voters of both parties.