Salt Lake County Mayor Ben McAdams said it was too early to respond to Pyle's criticisms.
The county earlier this month identified five potential sites for a new homeless shelter that would include 200 or more beds for an as-yet-unspecified homeless population.
Three sites are in West Valley City at 1820 W. Printers Row and 2411 and 2249 S. Winston St. and two more are in South Salt Lake. Salt Lake City has already sited proposed 200-bed shelters at 131 E. 700 South and 275 W. High Ave.
Legislation passed this session and signed by Gov. Gary Herbert requires the county to recommend a third site to the state's Homeless Coordinating Committee by March 30 and deprives city officials of any formal say in the matter.
But Pyle said there are options. West Valley City could try to derail the county's purchase of a selected property. It could sue. And it could simply be uncooperative "an unwelcome location with an unwelcome host," Pyle said to dissuade service providers from supporting the selected site.
"This issue is so important to us that we will go to whatever length we need to," Pyle said.
Asked if West Valley City would truly torpedo a collective plan for reducing homelessness that has been years in the making, Pyle said the question presumes "that we believe there's any chance for success in the first place."
A new shelter is likely to resemble the "overburdened and disastrous situation" at the emergency shelter at 210 S. Rio Grande St. in downtown Salt Lake City, said Pyle, who expounded in an op-ed he submitted to The Tribune last week.
Officials in both West Valley City and South Salt Lake have said their cities already take on a large share of the responsibility for reducing the county's homelessness.
West Valley City officials say they already have 33,000 units of affordable housing, while South Salt Lake officials have cited a handful of regionwide services that they say are already stretching thin their modest resources.
The public has two more chances to provide feedback: a 6 p.m. Tuesday open house at the Utah Cultural Celebration Center in West Valley City and a 6 p.m. Wednesday meeting of the county's site evaluation committee in Senate Building Room 210, at the state Capitol.
McAdams has said the county is open to considering other sites.
Pyle said West Valley City conducted its own search for sites that meet the county's criteria and found 40 throughout the valley, but that it won't present those to the county. That would give the impression that West Valley City was participating with the process, he said.
"Our calculations really are this: We're running out of time. We've got 10 days. [McAdams] continues to take this tenor that this is an open and legitimate process, which it is not."