The Multi-Scale Continuum and Line Exploration of W49 (MUSCLE W49) is a comprehensive gas and dust survey of the giant molecular cloud (GMC) of W49A, the most luminous star-formation region in the Milky Way. It covers the entire GMC at different scales and angular resolutions. In this paper we present: 1) an all-configuration SMA mosaic in the 230-GHz band covering the central 3 arcmin (10 pc, known as W49N), with most of the embedded massive stars; and 2) PMO 14m telescope observations in the 90-GHz band, covering the entire GMC with maps up to 35 arcmin in size, or 113 pc. We also make use of archival data from the VLA, JCMT-SCUBA, IRAM 30m, and the CSO BOLOCAM GPS. Our main findings are: 1) The W49 GMC is one of the most massive in the Galaxy, with a total mass ~1.1x10^6 Msun within a radius of 60 pc. Within a radius of 6 pc, the total gas mass is ~2x10^5 Msun. At these scales only 1% of the material is photoionized. The mass reservoir is sufficient to form several young massive clusters (YMCs) as massive as a globular cluster. 2) The mass of the GMC is distributed in a hierarchical network of filaments. At scales <10 pc, a triple, centrally condensed structure peaks toward the ring of HC HII regions in W49N. This structure extends to scales from ~10 to 100 pc. The W49A starburst most likely formed from global gravitational contraction with localized collapse in a hub-filament geometry. 3) Currently, feedback from the central YMCs (with a present mass Mcl > 5x10^4 Msun) is still not enough to entirely disrupt the GMC, but further stellar mass growth could be enough to allow radiation pressure to clear the cloud and halt star formation. 4) The resulting stellar content will probably remain as a gravitationally bound massive star cluster, or a small system of bound clusters. (ABRIDGED)
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