The nomenklatura were concerned that the weakness of the Soviet economy not become apparent, so they concentrated on visible achievements — rocket technology as exemplified by ICBMs and, yes, Sputnik, providing aid to their Fraternal Socialist Brethren such as Castro, and building a formidable military presence. Resources devoted to those ends had to be diverted from the weak economy, which weakened it further. The important fact about the American space program was not that it caught up to and exceeded Soviet capability; it was that the Americans did it out of pocket change — expenditures on Mercury, Apollo, etc., were huge in absolute numbers, but never required diversion of significant scarce resources from the consumer economy to support them. The same was true across the board. The United States could build aircraft carriers and ICBMs, deploy hundreds of thousands of troops and their equipment to Viet Nam, and send high-flying planes to take pictures of the Rodina, and suffer at worst some inflation and market distortion. The USSR could achieve much less than that, and that only by prying the last handful of grain from the most miserable peasant.
Certainly the weakness of the American economy is not apparent to the administration: every single piece of bad news is labeled as “unexpected.” Of course, there’s one major difference between the Moscow that was and the Washington that is: today, we have both nomenklatura and czars.