Selecting the first galaxies at z > 7 - 10 from JWST surveys is complicated by z < 6 contaminants with degenerate photometry. For example, strong optical nebular emission lines at z < 6 may mimic JWST/NIRCam photometry of z > 7-10 Lyman-break galaxies (LBGs). Dust-obscured 3 < z < 6 galaxies in particular are potentially important contaminants, and their faint rest-optical spectra have been historically difficult to observe. A lack of optical emission line and continuum measures for 3 < z < 6 dusty galaxies now makes it difficult to test their expected JWST/NIRCam photometry for degenerate solutions with NIRCam dropouts. Toward this end, we quantify the contribution by strong emission lines to NIRCam photometry in a physically motivated manner by stacking 21 Keck II/NIRES spectra of hot, dust-obscured, massive (logM(*)/M-circle dot.greater than or similar to 10-11) and infrared (IR) luminous galaxies at z similar to 1-4. We derive an average spectrum and measure strong narrow (broad) [O III](5007) and H alpha features with equivalent widths of 130 +/- 20 angstrom (150 +/- 50 angstrom) and 220 +/- 30 angstrom (540 +/- 80 angstrom), respectively. These features can increase broadband NIRCam fluxes by factors of 1.2 - 1.7 (0.2-0.6 mag). Due to significant dust attenuation (A(V) similar to 6), we find H alpha+[N II] to be significantly brighter than [O III]+H beta and therefore find that emission-line dominated contaminants of high -z galaxy searches can only reproduce moderately blue perceived UV continua of S-lambda alpha lambda(beta) with beta > - 1.5 and z > 4. While there are some redshifts (z similar to 3.75) where our stack is more degenerate with the photometry of z > 10 LBGs at lambda(rest) similar to 0.3-0.8 mu m, redder filter coverage beyond lambda(obs) > 3.5 mu m and farIR/submillimeter follow-up may be useful for breaking the degeneracy and making a crucial separation between two fairly unconstrained populations, dust-obscured galaxies at z similar to 3-6 and LBGs at z > 10.