The state of Nebraska will open a special session of the legislature on Tuesday afternoon in a last-gasp effort to stop or re-route the controversial Keystone XL pipeline project.

The pipeline, meant to carry crude from the tar sands of Alberta, Canada, to the refineries of Texas, has become a political liability for Barack Obama. He's been heckled during party fundraisers, and faces a big demonstration at the White House on 6 November.

For the next few days though, the focus shifts to Nebraska. Opponents of the pipeline are hoping this session of the legislature will find a legal means of re-routing the project away from an important source of ground water – or blocking it completely.

What happens in Nebraska could be critical for the future of the 1,660-mile pipeline. South Dakota – the state immediately north of Nebraska – said this week it would press TransCanada, the pipeline owner, for additional safety measures after learning that Nebraska had obtained similar concessions.

It was not immediately clear however how the legislature session would play out. The state's governor, David Heineman, has yet to introduce a proposal on resiting the pipeline. That lapse had some activists concerned on Monday.

"Normally when a governor calls a special session he introduces a bill, but the governor has not done that," said Jane Kleeb of Bold Nebraska, which has been leading the protests. "We are afraid that they will hold a special session and not pass anything and say they have done their best."

A state senator, Annette Dubas, is working on a separate proposal to give the state the authority to re-route the pipeline. There are also moves to try to block the pipeline by challenging TransCanada's methods for obtaining land use rights.

However, Kleeb said she was not confident the legislature would produce any legislation on the pipeline. "I think it's just a 50-50 shot at this point," she said.

The session, which opens on Tuesday afternoon, is expected to last at least two weeks.

But the biggest headache for Obama could well be the growing opposition to the pipeline from fellow Democrats. The Obama administration has yet to give formal approval for the project.

Officially, the decision on the pipeline falls to Hillary Clinton, the secretary of state. But pipeline opponents are trying to draw a direct line between Obama and the decision on Keystone.

Wealthy donors – the president was heckled at a high-dollar fundraiser in San Francisco last week – environmental groups, and young voters have all warned that the administration's stand on the pipeline could hurt him politically in next year's elections.

In a conference call with reporters, Michael Brune, the executive director of the Sierra Club, said: "I can say that we don't think we'll be able to effectively mobilise our members in the 2012 election cycle until the president stands up to big polluters," he said.

Some younger activists involved in the Keystone debate had a similar warning for Obama. "It's definitely going to have an effect on the 2012 election. A lot of young people right now are holding their breath and giving Obama one last chance to make good on his promise of change," said Abbie Rogers, 20, a student at the University of Mary Washington in Virginia, who was arrested in an anti-pipeline protest at the White House last August.

She said: "If Keystone XL goes through under his watch I think young voters are really going to have to make a decision whether or not they want to continue with an administration that seems to compromise early and often and that has done a lot that wasn't change – or at least nothing to the extent we felt we were being promised."

• This article was amended on 10 November 2011. The original misspelled the name of Annette Dubas as Anne Dubash. This has been corrected.