Blanton faced hitters for the first time Tuesday in a live batting practice session.
Scherzer faced hitters for the first time on Tuesday.
Zimmerman is 0 for 11 with two walks in six Grapefruit League games so far. More importantly, he's healthy.
Scherzer could pitch in a simulated or real game next.
Washington starter allows six runs across two innings against the Cardinals, but neither he nor his manager read much into it.
Unlike many franchises, the Nationals don't consider international players who sign at age 18 expired goods, and as a result, a handful are in big-league camp.
Wieters still hasn't appeared in a game after signing with the Nationals on Feb. 24.
The Nationals' ace threw 44 pitches across two simulated innings.
Lee was one of eight minor leaguers invited to big league camp for spring training.
The pitcher made his major league debut with the Nationals in 2007 and was the club's Opening Day starter twice.