Ruto has previously stated his intention to push through the Kenya Kwanza agreement in Parliament, with the most recent declaration being his plan to have the Budget revised downwards.
But coming a day before Wetang'ula rules on the majority side in the National Assembly, some opposition MPs read mischief in the president's visit.
Saboti MP Caleb Amisi said the timing of Ruto's visit could portray him as trying to intimidate Parliament.
"This is the first time we have seen a sitting president come to Parliament," Amisi said. "It goes without saying that he came to intimidate an arm of government and the speaker into making a favourable ruling."
Vihiga Senator Godfrey Osotsi said the president and speaker could have met for an "innocent lunch, but it could be viewed as canvassing".
"It is like when a judge is supposed to make a ruling in a matter you are involved in and you have lunch with the judge," Osotsi told The Standard Wednesday.
But Garissa Township MP Aden Duale dismissed such talk, saying that Ruto respects parliamentary leadership."The president just came to have lunch," he said. "He even had lunch with Azimio MPs."
"If the president wanted to intimidate the speaker he would have called him to his office, not Parliament," Kimilili MP Didmus Barasa said.
"Those Azimio MPs are just trying to be relevant."
Sabatia MP Clement Sloya (UDA) said: "Ruto's impromptu visit to Parliament was a show of unity with his MPs. It was in no way an act of intimidation to those in Azimio. He was there to assure his troops that regardless of the outcome of tomorrow's (today's) ruling, he knows that Kenya Kwanza is the majority coalition in the House."
"I'm sure were it the leader of Azimio coalition party Raila Odinga visiting it wouldn't have been considered as intimidation rather than a show of support to his members," he added.
Ruto has faced criticism from the opposition over alleged plot to muzzle Parliament following a wave of defections from Azimio to Kenya Kwanza after the August 9 General Election.
Azimio and Kenya Kwanza MPs locked horns on the majority issue during Tuesday's sitting, each keen to sway the Speaker to rule in their favour.
Kenya Kwanza MPs, led by Kikuyu Town MP Kimani Ichung'wa asserted that Azimio was not a coalition and it had suffered defections.
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Azimio's counterargument majorly centred on their claim that several parties said to have defected, such as the Movement for Democracy and Growth and the United Democratic Movement, had not moved out lawfully.
Ugunja MP Opiyo Wandayi said Azimio was a coalition and a party.
He also argued that the Registrar of Political Parties had settled the matter by informing the National Assembly Clerk which coalition was the majority.
Alego Usonga MP Sam Atandi said he expected the speaker to make a partisan decision. "The speaker is a principal in Ford Kenya. It is not feasible that he will make a ruling against his coalition," Atandi said.
He said Wetang'ula's dismissal of Azimio agreement tabled by Suna East MP Junet Mohamed on Tuesday was an indication of how he would rule.