Former Fine Gael TD Denis Naughten says the public are turning to Independents because they have "had enough" of political point scoring.
The Roscommon/South Leitrim Deputy says the Dáil chamber is losing relevance to ordinary people's lives.
It comes after two independents won the by-elections over the weekend.
Anti Austerity Alliance candidate Paul Murphy topped the poll in Dublin South West, while Independent Michael Fitzmaurice fought off competition from Fianna Fáil in Roscommon South Leitrim.
Mr Naughten said: "We now have a gang of four - the Taoiseach, the Tánaiste, the Minister for Finance and the Minister for Public Expenditure and Reform - making all the decisions.
"They are rubber-stamped by the Cabinet and they are rammed through a Dáil that is bickering and point-scoring.
"I think people are seeing through that now and they have just had enough."