The Blues went to stumps on day two at 4-235 at the SCG, with Kurtis Patterson out for 99 just before close in reply to Tasmania's first-innings 364.
Patterson's runs and Webster's form have come in the background of Australia's first-Test embarrassment against India in Perth.
If changes do come before the second Test in Adelaide, it is likely to be Josh Inglis who comes into the side as the current reserve bat and pressure on Marnus Labuchagne.
But there is a case to be made for Webster.
The Tasmanian was the leading run-scorer in the Sheffield Shield last summer, and his 61 on Monday helped take his red-ball season record to 401 runs at 57.29.
Included in that are unbeaten scores of 61 and 41 for Australia A against India A in the past month.
Webster brought up his 50 off 66 balls on Monday, after two cover-drives went to the rope early in the day against Jackson Bird.
Another boundary came from a clever paddle-sweep off Adam Zampa, before he was caught behind off Bird shortly after lunch as part of a collape of 3-0.
The other factor in Webster's favour are the overs he can offer with the ball as both a seamer and spinner.
Bowling workloads have suddenly become crucial after Cameron Green's injury, and the use of Labuschagne to shoulder some of the load in Perth.
The 30-year-old trapped Maddinson lbw for 34 on Monday with his medium-pace, before having Oliver Davies and Patterson caught behind in his 3-56.
He also had two catches dropped off his bowling.
For now though, Webster is resigned to the fact Australia are unlikely to go away from their set up of three specialist quicks and only the one allrounder in Mitch Marsh.
"It seems like they are pretty traditional with three quicks, spin and allrounder for a lot of years," Webster said.
"Those big three quicks are very hardened and bowl a lot of overs, and Nathan is unbelievable (with his workload).
"That's usually the way they go, I don't see them going any other way.
"My way in is if someone does need a rest, or God forbid an injury. You never wish that on anyone. But that is a way I might find my way in the squad at least."
Patterson is also starting to make something of a selection case, with this his fourth straight score above 50 since being recalled to the NSW team.
A Test player who scored a century in his last match back in 2019, the left-hander has made scores of 91, 66, 71 and 99 for the Blues this summer.
Earlier Konstas had looked particularly good for the Blues, cover-driving anything too full to the boundary before chopping on a cut shot on 39.
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