To the millions of Americans fed up with Washington gridlock, there were a few encouraging signs following Tuesday’s elections that shifted control of the U.S. Senate to Republicans.

Having survived a tough reelection challenge in Kentucky, Mitch McConnell, Senate Republican leader, reflected on the future with a GOP-controlled Senate. Saying there doesn’t have to be “perpetual conflict,” McConnell said Congress and the White House “have an obligation to work together.”

Reacting to McConnell words, political analysts pointed out that tea party-affiliated senators, including Ted Cruz of Texas, might block any efforts by McConnell to compromise with Democrats and the White House, just as tea party-linked members of the House of Representatives prevented Majority Leader John Boehner from striking a deal with President Barack Obama during the debt ceiling crisis.

McConnell will preside over a Senate with several members eyeing a run for the White House in 2016 and not wanting to tarnish a conservative record with any compromise votes.

McConnell’s legislative and tactical skills will be tested if he’s serious about moving away from perpetual conflict and finding ways to work with Democrats and Obama.

The other encouraging sign emerging late Tuesday evening came from the White House with the president requesting a meeting with the leaders of both parties from the House and the Senate at the White House on Friday afternoon. This meeting could offer a chance for a new start, to lay the foundation for finding common ground. Accepting that Republicans will have full control of Congress in January, he can offer a determination to get things done in the final two years of his administration.

Having been accused of being nothing more than the “party of no,” Republicans will soon have to decide if they want to continue to block any and all initiatives from Obama and congressional Democrats. They should understand that most voters are tired of partisan bickering blocking action.

If Republicans hope to avoid an Election Day reversal of fortunes in 2016 when they have many more seats to defend, then they need to show that they can govern and to explain what they stand for.

Republicans “need to show leadership ahead of politics,” according to conservative columnist Charles Krauthammer, who also said the GOP needs not only to have an agenda, but to pass bills reflecting that agenda. Talk alone will not convince voters that Republicans can govern and get things done.

For his part, Obama faces an even tougher environment than he’s had with a Republican-controlled House. He will no longer have Senate Majority Leader Harry Reid refusing to bring up GOP-passed bills from the House, thus preventing them from reaching Obama’s desk.

Some say Obama’s job will go from difficult to near impossible. But it’s been noted that President Bill Clinton faced a hostile Congress controlled by Republicans during his final two years and he managed to produce welfare reform and a balanced budget.

Areas where compromise should be possible include infrastructure investment — fixing roads, bridges, railway and ports. Historically, both parties support funding this critical work, and Republicans, with their philosophical faith in private business, should also support the idea of an infrastructure bank that allows tax dollars to be leveraged with private money to expand the amount of road and bridge work being done.

There also should be common ground in tax reform. Both parties know that the federal tax code is overly complicated and littered with loopholes. Republicans complain that the U.S. economy is hurt by having the highest corporate tax rate in the world. But that’s not the whole story, since many large corporations pay an effective tax rate far below the official rate of 28 percent by using many tax breaks and credits. Leaders of both parties have said corporate tax rates can reduced by eliminating many tax deductions and loopholes. If Republicans want to show they can get things done, they should produce a plan to do just that — reduce tax rates while also trimming exemptions, deductions and loopholes to make up for the lost tax revenue.

Starting in January, Republicans will have an opportunity to play politics and be the “party of no” — or they can find ways to compromise and get things done, proving they can govern.