Tip's right that we do have some dry air to contend with for much of the area, but the strong jet is going to induce some late advection. The GFS is trying to bring in a swath of low level moisture and pressure advection late Tuesday.
The pressure advection is kind of weird though, basically pressures on the isentropic surfaces are falling so quickly behind the front that SW flow behind the front is actually blowing from high to low pressure (i.e. ascent). Normally you get pressure advection due to wind blowing normal to isobars, not from local changes in pressure. So you can see why these set ups are tenuous.