While McConnell congratulated President Barack Obama on his re-election, the Kentucky Republican showed no inclination to concede any political ground, The (Louisville) Courier-Journal reported.
"The American people did two things: They gave President Obama a second chance to fix the problems that even he admits he failed to solve during his first four years in office, and they preserved Republican control of the House of Representatives," McConnell said in a statement.
"The voters have not endorsed the failures or excesses of the president's first term, they have simply given him more time to finish the job they asked him to do together with a Congress that restored balance to Washington after two years of one-party control.
"Now it's time for the president to propose solutions that actually have a chance of passing the Republican-controlled House of Representatives and a closely divided Senate, step up to the plate on the challenges of the moment, and deliver in a way that he did not in his first four years in office.
"To the extent he wants to move to the political center, which is where the work gets done in a divided government, we'll be there to meet him half way."
McConnell said a starting point would be to find a way to avoid taking the federal government over the "'fiscal cliff' without harming a weak and fragile economy." The next step, he said, would be to reform the tax code "and our broken entitlement system."
U.S. House Speaker John Boehner, R-Ohio, offered a similar assessment in Washington Wednesday.
Republicans picked up one Senate seat in Nebraska but lost seats in Maine, Massachusetts and Indiana -- dashing their hopes of wresting control away from the Democrats.
The Democrats retained an open seat in Virginia, where Tim Kaine held off a strong challenge by Republican George Allen, CNN projected. Kaine held a 51-49 edge with 86 percent of the vote counted.
GOP state lawmaker Deb Fischer defeated Democrat Bob Kerrey, a former U.S. senator and Nebraska governor, for the seat given up by Democrat Ben Nelson. CNN said Fischer had 55 percent of the vote to 45 percent for Kerrey with 44 percent of precincts tallied. Fischer had led in the polls throughout the campaign, though Kerrey had closed the gap heading into Election Day.
Maine independent Angus King defeated GOP nominee Charlie Summers and Democrat Cynthia Dill, MSNBC projected. King had 51 percent of the vote to 28 percent for Summers and 6 percent for Dill with 14 percent of precincts counted, CNN reported.
In winning the seat being vacated by retiring Sen. Olympia Snowe, King was generally expected to caucus with the Democrats if elected, though that remained to be seen.
MSNBC also projected Democrat Elizabeth Warren as the winner over Republican incumbent Scott Brown in Massachusetts. Warren had 53 percent of the vote to 47 percent for Brown with 44 percent of precincts in, CNN said.
In Indiana, the seat held by Republican Sen. Richard Lugar went to the Democratic column, with MSNBC projecting Joe Donnelly the winner over Republican Richard Mourdock. Donnelly led Mourdock 49-45 with 75 percent of the vote in, CNN reported.
Mourdock knocked off Lugar in the GOP primary but got into hot water with comments during a debate that he is opposed to abortion in the case of pregnancies resulting from rape because they are "something that God intended to happen."
In Arizona, Jeff Flake kept the seat being given up by Sen. Jon Kyl in the Republican column by defeating Democrat Richard Carmona 51-45 with 57 percent of the precincts counted, CNN said.
In New Mexico, Democratic Rep. Martin Heinrich was projected by MSNBC to be the winner over Republican former U.S. Rep. Heather Wilson for the seat held by the retiring Democrat Jeff Bingaman.
The GOP also was unable to unseat first-term Democratic incumbent Sen. Sherrod Brown, who defeated Republican challenger Josh Mandel, the state treasurer and Iraq war veteran who was saddled with Ohio Politifact's "Pants on Fire" rating for his campaign rhetoric -- including unsubstantiated claims that votes cast by Brown were responsible for Ohio jobs being moved to China.
Brown held a 51-43 lead with 44 percent of the precincts counted, CNN said.
In Missouri, Democratic Sen. Claire McCaskill fended off her Republican challenger, U.S. Rep. Todd Akin, who had problems with his comments on abortion and rape. MSNBC called her the winner.
CNN said McCaskill was ahead of Akin 55-39 with 20 percent of precincts counted.
Akin worked his way back into contention after his campaign took a heavy blow when he suggested women who have been raped have a biological defense against pregnancy.
By late Wednesday, incumbent Democratic Sen. Jon Tester in Montana and Democrat Heidi Heitkamp in North Dakota were declared winners of their Senate races.
The balance of power in the Senate shifted slightly in favor of Democrats, even though they were defending twice as many seats as Republicans, The Hill reported.
Heading into the elections, Democrats held 51 seats and were joined by two independents in their caucus. Republicans control 47 seats.
NBC said after the day's elections Democrats held 51 seats with independent Bernie Sanders of Vermont generally siding with them.
In Wisconsin, U.S. Rep. Tammy Baldwin defeated former Gov. Tommy Thompson, NBC projected, becoming the state's first U.S. senator and the upper house's first openly gay member.
NBC said Democrat Rep. Mazie Hirono won the seat being vacated by Daniel Akaka in Hawaii and projected Sens. John Barrasso, R-Wyo., Maria Cantwell, D-Wash., Ben Cardin, D-Md., Bob Casey, D-Pa., Bob Corker, R-Tenn., Dianne Feinstein, D-Calif., Kirsten Gillibrand, D-N.Y., Joe Manchin, D-W.Va., Robert Menendez, D-N.J., Debbie Stabenow, D-Mich., Sheldon Whitehouse, D-R.I., and Roger Wicker, R-Miss., all won re-election.