Slovenia, like the other euro states, has to ratify the EFSF reform. The vote had been scheduled for September 27, and the finance ministry has said that it is keen to stick to that timetable.
"It calls into question whether, in the middle of this political turmoil in Slovenia, it will be able to do that," Zachary Rothstein, an analyst at Control Risks, told CNBC.com.
The president or parliament now have to nominate a new prime minister; they have 30 days to confirm the appointment, or parliament faces dissolution and early elections.
"It's highly unlikely that the president will nominate someone or that parliament will support them, because all opposition parties want early elections. The strongest opposition party, the Democratic Party (SDS) is doing well in the polls, better than its current representation in parliament, so it's pushing for early elections," Rothstein said.
The SDS would be likely to win in a snap election, which may cause concern in Brussels. The party's leader, Janez Jansa, has publicly opposed bailouts and support mechanisms for Greece.
"Parliament can still function, but there's a risk that because elections have come closer, issues could become more politicized than it would have been otherwise," Rothstein said. "In this case, I think it's unlikely that the parliament would fail to ratify the mechanism."
In opposition, Rothstein noted, it is easier to make populist statements, and this may be curtailed by the high likelihood of making it into government.
"I think that because his party is likely to form the next government and he is likely to be the next prime minister, he will face enormous pressure to approve the mechanism and I think he wouldn't want to jeopardize the country's reputation at this stage."
Jansa may choose to have his party abstain on September 27, clearing the path for the reform to pass without visibly backing an unpopular cause.
However, analysts note that the small size of the parliament and the potential for a more politicized vote could see the risk of an upset creeping in at the margin.
Likewise, with Austria, Finland, the Netherlands and Slovakia also likely to ramp up the noise around their own parliamentary processes and play brinkmanship with Brussels, the market may find many more reasons to be jittery ahead of the final approval of the mechanism's reform.