AUGUSTA — Democratic state lawmakers sought to pressure Republicans to support a compromise on a new congressional map Monday, a day before a special legislative session on the issue. But even as negotiations continued, key lawmakers acknowledged that the issue could wind up back in the courts.

A panel of federal judges ordered the Legislature in June to redraw the line dividing Maine’s two congressional districts to balance the populations of the districts according to 2010 census data.

A Republican-backed plan that was narrowly rejected by a bipartisan commission in August is seen as the best opportunity for the GOP to pick up Maine’s 2nd District House seat, which has been held by Democrats since 2003.

Majority Republicans and Democrats have proposed a succession of new district maps, but a plan with bipartisan support has remained elusive. Republicans have threatened to use their majority to push through a plan they favor on a simple majority vote.

Democrats claimed Monday that would be hypocritical, because several Republicans championed a proposed constitutional amendment earlier this year that says any future reapportionment plan would require a two-thirds vote of approval.

The constitutional amendment will be up for a public vote Nov. 8.

“Republicans are threatening to not respect the very amendment they passed this spring,” said Democratic Rep. Maeghan Maloney of Augusta. “It is as if the Republican Party has amnesia and thinks we will tolerate this hypocrisy.”

Another Democrat, Rep. Anne Graham of North Yarmouth, joined Maloney “to tell voters to reject the bullying tactics” of Republicans.

Earlier in the day, the state GOP fired off emails to party members asking them “to call your legislator and tell them to vote for the Republican plan and stop gerrymandering with our future.”

The Maine People’s Alliance, which usually sides with Democrats, emailed its own warning of a GOP plan to “radically redraw the congressional districts in Maine, moving 360,000 Maine people, seven counties, and 139 municipalities from one district to another.” It, too, asked recipients to call their legislators.

Despite the back-and-forth, both parties professed optimism that a single plan could be formulated, although Republicans wouldn’t rule out pushing through a plan with a simple majority.

A GOP negotiator, Rep. Kenneth Fredette of Newport, rejected Democrats’ charge of hypocrisy and bullying and said his party takes seriously the court order to adopt a redistricting plan.

“It’s not a process of bullying. It’s a process of math,” Fredette said as his party offered two new maps for Democrats’ consideration.

The judges gave the Legislature until Sept. 30 to finish its redistricting work. If the Legislature can’t complete the task, the Maine Supreme Judicial Court will have until Nov. 15 to do it, as it did a decade ago when lawmakers failed to adopt a plan.

The order says that if a redistricting plan based on 2010 census data isn’t adopted within those deadlines, a federal court will proceed with its own revision of the political map.

Fredette and Democratic Rep. John Martin of Eagle Lake both acknowledged that the matter could end up in court.