Agreeing with Chickee, he's also using a volume control pedal for swells to eliminate the attack of the notes. In the studio I get this effect with a Helix modeler. I'm using a Deluxe Reverb model with the volume up around one o'clock with a 2x12" Twin cab model for more smoothness. I run it through the volume pedal model then a plain-Jane MXR Dyna-Comp compressor model and then, depending on how much drive I want, say a little more David Gilmour territory, a Prince of Tone* model. Then it is the amp and cab models with my special sauce of post-cab EQ and then delay digital and a room reverb.
I use a heavy Shubb SP3 Sally Van Meter ergo steel. If you pick the strings with the right hand up a little over the fingerboard and roll off a pinch of tone at the guitar you get a rounder sound.
The cool part is that with the volume pedal before a cranked, medium gain non-master volume amp you can choose just how far you want to push into amplifier distortion. Just a little? Make it growl? Fairly clean? All in the pedal and not fizzy.
I've got three guitars to choose from. I'd probably go with my inexpensive Gretsch Electromatic G5715 lap steel for this effect because it is the smoothest I've got, even more than my pre-war Richenbacher B.
Gretsch has changed the guitar numbers (G5700) and colors but it is the same guitar,
HERE. It is a modern version of their classic 1950s 6147
Mainliner.
Bob
* The MXR/Jim Dunlop licensed "Duke of Tone" clone should be out soon.