We investigate the relation between star formation rate (SFR) and gas surface densities in Galactic star-forming regions using a sample of young stellar objects (YSOs) and massive dense clumps. Our YSO sample consists of objects located in 20 large molecular clouds from the Spitzer cores to disks (c2d) and Gould's Belt (GB) surveys. These data allow us to probe the regime of low-mass star formation, essentially invisible to tracers of high-mass star formation used to establish extragalactic SFR-gas relations. We estimate the gas surface density ( Delta *Sgas) from extinction (AV ) maps and YSO SFR surface densities ( Delta *SSFR) from the number of YSOs, assuming a mean mass and lifetime. We also divide the clouds into evenly spaced contour levels of AV , counting only Class delta and Flat spectral energy distribution YSOs, which have not yet migrated from their birthplace. For a sample of massive star-forming clumps, we derive SFRs from the total infrared luminosity and use HCN gas maps to estimate gas surface densities. We find that c2d and GB clouds lie above the extragalactic SFR-gas relations (e.g., Kennicutt-Schmidt law) by factors of up to 17. Cloud regions with high Delta *Sgas lie above extragalactic relations up to a factor of 54 and overlap with high-mass star-forming regions. We use 12CO and 13CO gas maps of the Perseus and Ophiuchus clouds from the COMPLETE survey to estimate gas surface densities and compare to measurements from AV maps. We find that 13CO, with the standard conversions to total gas, underestimates the AV -based mass by factors of ~4-5. 12CO may underestimate the total gas mass at Delta *Sgas 200 M pc--2 by 30%; however, this small difference in mass estimates does not explain the large discrepancy between Galactic and extragalactic relations. We find evidence for a threshold of star formation ( Delta *Sth) at 129 ? 14 M pc--2. At Delta *Sgas> Delta *Sth, the Galactic SFR-gas relation is linear. A possible reason for the difference between Galactic and extragalactic relations is that much of Delta *Sgas is below Delta *Sth in extragalactic studies, which detect all the CO-emitting gas. If the Kennicutt-Schmidt relation ( Delta *SSFR Delta *S1.4 gas) and a linear relation between dense gas and star formation are assumed, the fraction of dense star-forming gas (f dense) increases as ~ Delta *S0.4 gas. When Delta *Sgas reaches ~300 Delta *Sth, the fraction of dense gas is ~1, creating a maximal starburst.