  We present deep Chandra X-ray observations of two nearby Type Ia supernovae,
SN 2017cbv and SN 2020nlb, which reveal no X-ray emission down to a luminosity
$L_X$$\lesssim$5.3$\times$10$^{37}$ and $\lesssim$5.4$\times$10$^{37}$ erg
s$^{-1}$ (0.3--10 keV), respectively, at $\sim$16--18 days after the explosion.
With these limits, we constrain the pre-explosion mass-loss rate of the
progenitor system to be $\dot{M}$$<$7.2$\times$10$^{-9}$ and
$<$9.7$\times$10$^{-9}$ M$_{\odot}$ yr$^{-1}$ for each (at a wind velocity
$v_w$=100 km s$^{-1}$ and a radius of $R$$\approx$10$^{16}$ cm), assuming any
X-ray emission would originate from inverse Compton emission from optical
photons up-scattered by the supernova shock. If the supernova environment was a
constant density medium, we find a number density limit of n$_{CSM}$$<$36 and
$<$65 cm$^{-3}$, respectively. These X-ray limits rule out all plausible
symbiotic progenitor systems, as well as large swathes of parameter space
associated with the single degenerate scenario, such as mass loss at the outer
Lagrange point and accretion winds. We also present late-time optical
spectroscopy of SN 2020nlb, and set strong limits on any swept up hydrogen
($L_{H\alpha}$$<$2.7$\times$10$^{37}$ ergs s$^{-1}$) and helium ($L_{He,
\lambda 6678}$$<$2.7$\times$10$^{37}$ ergs s$^{-1}$) from a nondegenerate
companion, corresponding to $M_{H}$$\lesssim$0.7--2$\times$10$^{-3}$
M$_{\odot}$ and $M_{He}$$\lesssim$4$\times$10$^{-3}$ M$_{\odot}$. Radio
observations of SN 2020nlb at 14.6 days after explosion also yield a
non-detection, ruling out most plausible symbiotic progenitor systems. While we
have doubled the sample of normal type Ia supernovae with deep X-ray limits,
more observations are needed to sample the full range of luminosities and
sub-types of these explosions, and set statistical constraints on their
circumbinary environments.
