MLAs have spent most of Tuesday debating the welfare reform bill, which has reached the consideration stage in Stormont's legislative process.
The day's proceedings adjourned at 22:00 GMT but will resume on Wednesday.
Welfare reform had caused an impasse until a deal was reached at December's inter-party talks in Stormont House.
Politicians agreed to set aside tens of millions of pounds for a fund designed to provide financial support for those adversely impacted by welfare changes.
Mr Robinson said the financial cost of not implementing welfare reform would have been at such a level that "we could not have sustained an executive".
He said that other parties could not have an "a la carte" approach to the Stormont House Agreement.
"If people genuinely want to move forward in Northern Ireland, then it is important this legislation goes through. It's important that the parties uphold the agreement that all of us reached," he said.
At the start of the debate, the DUP was accused of "killing off discussion" of the bill.
Ulster Unionist Roy Beggs said the DUP had done so by  tabling a series of petitions of concern against amendments to the bill.
"They have displayed the undemocratic nature of their attitudes as MLAs and the undemocratic nature of their party, which of course has the word democracy in their name," he said.
Mr Robinson rejected Mr Beggs' claim that his party's actions were "shameful".
The measure was designed as a way to safeguard minority rights in Stormont's power-sharing assembly.
If a petition of concern is presented to the assembly speaker, any motion or amendment will need cross-community support.
In such cases, a vote on proposed legislation will only pass if supported by a weighted majority (60%) of members voting, including at least 40% of each of the nationalist and unionist designations present and voting.
Effectively this means that, provided enough MLAs from a particular community agree, that community can exercise a veto over the assembly's decisions.
Apart from the amendments tabled by Social Development Minister Mervyn Storey of the DUP, only two others - put forward by the UUP - survived.
However, Mr Robinson, the first minister, said assembly members were still capable of discussing the bill as well as the amendments.
The SDLP's Alex Attwood accused the DUP of trying to run a "coach and horses" through the amendments.
"Never before in the life of the chamber has there been such a swingeing attempt through petitions of concern to shut down what might be good law for the people of this part of the world," he said.
Sinn Féin's Martin McGuinness said some SDLP assembly members were defying their party leader Alasdair McDonnell by tabling the amendments in the chamber.
"The SDLP dissidents are clearly now in charge of the party and are prepared to risk the collapse of the Stormont House Agreement - and thereby the power-sharing institutions themselves - for the sake of party political grandstanding," he said.
Generally, Northern Ireland Assembly bills reach their consideration stage a few months after MLAs first debate their principles.
The fact that two years and four months have passed since this bill was last on the floor of the chamber shows just how difficult the arguments over welfare reform have been.
However, the essential deal was struck before Christmas, with the parties accepting the introduction of universal credit and personal independence payments, to replace benefits such as jobseeker's allowance, tax credits and disability living allowance.
Stormont is providing support for those adversely impacted financially by the changes to the welfare system by setting aside nearly £30m to assist claimants who lose out in 2015/16.
Sinn Féin has claimed the fund will amount to more than £500m over the next six years.
First Minister Peter Robinson has told MLAs the Northern Ireland Assembly would have "gone down" if there had been no agreement on welfare reform.