ST. PAUL (AP) — Minnesota leaders said Friday evening they were on the brink of a session-ending deal that would mean curbs on local property taxes, extra dollars for schools and the elimination of a nearly $1 billion budget deficit.

A few details still needed to be firmed up, but lawmakers from both parties indicated a conceptual agreement was almost nailed down. House Speaker Margaret Anderson Kelliher predicted flatly that session would end before sunrise on Sunday.

‘‘This is a situation where the train is picking up speed. As the train picks up speed and leaves the station it’s going to be harder and harder for things to get in the way of stopping it,’’ Kelliher said as she and others emerged from a meeting with Pawlenty.

She extended her train analogy to voice confidence that the final deal will also include state money toward a proposed Minneapolis-to-St. Paul light rail line.

Her positive take was shared by Pawlenty as he left the Capitol for an evening speech to Wisconsin Republicans. He was due back later Friday.

‘‘We’re close,’’ he said. ‘‘We’ve got to work out the pieces. If it’s going to happen, it could happen tonight or tomorrow morning. But it looks like it could happen tonight.’’

Added House Minority Leader Marty Seifert, R-Marshall: ‘‘There would have to be something really major to happen to unravel things.’’

Things were pushing in the direction of a handshake agreement all day.