Late Tuesday, all four leaders the Alliance agreed to attend. But the likelihood of the two blocs reaching an agreement remained unsure.
Earlier in the evening, Center Party leader Annie Lööf told news agency TT that "it is Prime Minister Stefan Löfven's responsibility to find a solution now."
Calling the current situation "serious", Löfven offered an outstretched hand to the four party leaders and said they would bear responsibility if the Sweden Democrats had their way. He also made it clear he was prepared to make concessions in his party's budget.
"Are they [the Alliance] prepared to cooperate with the government on the budget?" Löfven asked at a news conference. "Or are they prepared to govern with the support of the Sweden Democrats?"
The premier said it was "high time" to leave behind the bickering of September's national election and instead focus on what is best for Sweden.
Less than an hour before Löfven's comments, the Sweden Democrats announced they would support the center-right opposition bloc's budget, effectively sinking the Social Democrat-led government's proposal in a vote due on Wednesday.
Löfven hopes the eleventh-hour talks could produce a new budget that both the Alliance and the government could agree on.
The prime minister also had sharp words for the Sweden Democrats, accusing them of putting politics and strategy before the good of the nation.
The Sweden Democrats "have acted in an exceptionally irresponsible manner," he said.