The DUP encouraged Sinn Féin to "come back from the brink".
Outstanding issues include Sinn Fein's demand for legislative protections for Irish language speakers and the party's insistence that DUP leader Arlene Foster can not return as First Minister while a public inquiry into a botched green energy scheme is ongoing.
Ulster Unionist (UUP) leader Robin Swann said his party would not provide "cover" for the DUP if it signed up to an Irish Language Act.
It is nearly six months since the late Martin McGuinness dramatically resigned as Deputy First Minister, collapsing the power-sharing administration.
"The DUP have not moved on any of the substantive issue which sit at the heart of this crisis", he said.
Failure to strike a powersharing deal in Northern Ireland would have "profound and serious" implications, the British Government has warned.
Northern Ireland has remained without a devolved government since March 2, when a snap election returned an indecisive result. A number of attempts to restore powersharing in the wake of that poll floundered, with three UK Government deadlines for a deal having already been missed.
The parties have until 4pm on Thursday to restore a devolved executive or Northern Ireland faces the prospect of a return of direct rule from London.
The Glasgow Central MP addressed her concerns to Northern Ireland Secretary of State James Brokenshire during the first Northern Ireland Questions session of the new parliament.
Speaking on the eve of the deadline, SF negotiator John O'Dowd said the issue was the time-scale but the willingness by the participants in the talks to resolve the outstanding issues.
"I would encourage Sinn Fein to be mature, no high-wire acts, let's get down to work, knuckle down and find a way through this, and it is possible if people apply themselves". "If Sinn Fein continue to mess about I think they will pay a heavy price". "They haven't moved on any of the fundamental rights and equality issues that require to be embraced".
"We want to show absolute respect to people's language and culture and are working extremely hard to identify what people's bottom lines are and how we can move those issues forward". Sinn Féin have identified language as their highest priority.
Ms Thewliss wanted to know how the Conservative government could act with impartiality between unionists and Irish nationalists in Northern Ireland, given its dependence on the support of the DUP.