They did, but overstepped the mark by trying to build a mach 3 design, which actually turned out to be good thing in the end as the problems in building a commercial carrier which could get through the thermal barrier slowed them down long enough so that the low cost market become the established norm rather than the jet set and captains of industry market that originally drove the design for Concorde.
Actually they were fairly clear from early on that the US SST would be titanium based to avoid stagnation temp issues. The side effect of that was they were looking at a 600,000lb AUW.
The basis of the protests against Concorde on either side of the pond was primarily sonic booms. Research from Langley into the kind of overpressure that would result from a 600,000lb aircraft at M3 told them that the public would never accept it. The USAF was already paying several million in compensation for sonic boom damage back in the early 60s from small fighters.
The administration eventually pulled the plug rather than face the growing political opposition.