Is this true? "If there are no weather front or severe weather systems, then the dew point within a single day is fairly constant, no matter how large the day/night temperature variation."
If you consider a closed system, this will be true, as dewpoint is related to the absolute moisture which is not a function of temperature. However, as Fred's answer demonstrates, the atmosphere is not a closed system. Even devoid of fronts and severe weather there are still pressure gradients which result in wind. Wind advects moisture and so if there is wind the moisture (dew point) can change.
Furthermore if we consider surface fluxes that statement becomes even less true. With no advection if we have vegetation or standing water on the surface we can increase the dew point just through evapotranspiration.
From a review of weather observations, that statement is false.
Below are the synoptic weather maps for Australia for 11 August 2015 and 12 August 2015. There are no weather fronts, or adverse weather in the western two-thirds of the continent.
Alice Springs (lat:-23.8, long: 133.89) is in the centre of the continent. It's weather observations for 11 August 2015 reveal the temperature ranged between $5.8$ $^oC$ and $26.0$ $^oC$ and the dew point range was between $-18.8$ $^oC$ and $-2.5$ $^oC$.
Similarly for Darwin (lat: -12.42, long: 130.89), which is located on the coast in the sub tropics, in the central north of the country, the temperature range for 11 August 2015 was $19.7$ $^oC$ to $30.1$ $^oC$, while the dew point range was $15.4$ $^oC$ to $19.8$ $^oC$.
Perth (lat: -31.93, long: 115.98), on the southern western coast has a temperate Mediterranean climate. It's temperature range was $10.2$ $^oC$ to $17.6$ $^oC$ and the dew point range was $5.7$ $^oC$ to $11.7$ $^oC$.
Adelaide (lat: -34.95, long: 138.52), on the southern coast, in the centre region , also has a temperate climate and its temperature ranged from $7.6$ $^oC$ to $15.4$ $^oC$ and the dew point range was $-0.3$ $^oC$ to $8.5$ $^oC$.
Lastly, Brisbane (lat: -27.39, long: 153.13) which is on the east coast had temperatures between $8.2$ $^oC$ and $21.9$ $^oC$ and the dew point varied between $6.9$ $^oC$ and $15.8$ $^oC$.
All these weather observations show significant variance in the dew point for these locations given the respective temperature ranges and the lack of weather fronts and adverse weather systems.