There were 201 House and Senate seats in play Tuesday, but a switch of just 11 seats would give the DFL control of the Legislature, the (Minneapolis) Star Tribune reported.
Republicans held a 37-30 majority in the state Senate coming into the election. The GOP advantage in the House was 72-62.
DFL Chairman Ken Martin said late Tuesday it was too soon to say whether the party would take control of the Legislature, but he told the newspaper it looks like that will be happen if the trend line continued.
"We saw an amazing turnout around the country and around the state for President Obama and the reality is that that's going to translate into votes for our legislative candidates," Martin said.
Incomplete returns late Tuesday suggested Democrats appeared set to take control of the Colorado House from Republicans, who held a 33-32 majority prior to the election. If Democrats succeed in taking the majority, Mark Ferrandino of Denver is likely to become the first openly gay speaker of the Colorado House, The Denver Post reported.
Democrats held a 20-15 lead in the state Senate going into the election.
In California, Democrats were trying to increase their majorities in the Assembly and the state Senate -- and perhaps put together a supermajority in the Senate.
Republicans in Sacramento have been able to stop Democrats from raising taxes because tax increases require a two-third majority vote in the state Senate. If Democrats manage to get a supermajority after all the ballots are counted, party leaders say they will be able to raise revenues as part of an approach to dealing with the state's chronic budget deficits.
"With a working two-thirds majority, the Senate can move California forward without running headlong into a recalcitrant minority party who place ideology above balanced solutions that spur job growth," Democratic state Sen. Darrell Steinberg said.
Maine Democratic Party Chairman Ben Grant said early Wednesday Democrats think they have won 17 seats in the state Senate, but the Bangor Daily News said it was too soon to know whether Democrats had regained control of the chamber.
One highlight of the Maine election was the defeat of state Rep. John Martin, who had served in the Legislature for 48 years -- including nearly two decades as speaker of the state House of Representatives, from 1974-1995.
Democrats held on to their lead in the Oregon Senate and regained control of the House, in part because four freshmen Republican members lost their bids for re-election, The (Portland) Oregonian reported.