Republicans have tried to pin the lame duck label on President Obama for quite a while now. But for a lame duck, Obama is doing pretty well.

He won on Obamacare. He won on gay marriage. He won on trade. His party was even able to leverage a horrendous crime — the killings in Charleston — to put Republicans on the defensive over the Confederate flag.

A president’s approval rating, and his general image of success or failure, affect the candidate of his party seeking to succeed him. From that perspective, Obama’s victories are a gift to Democratic frontrunner Hillary Clinton.

Indeed, Clinton was quick to embrace the Supreme Court Affordable Care Act decision. “Yes!” she tweeted just minutes after the news broke. “SCOTUS affirms what we know is true in our hearts & under the law: Health insurance should be affordable & available to all.”

A short time after Clinton’s statement, I sent notes to several Republican operatives, some working on presidential campaigns and some unaffiliated. How do GOP candidates deal with a president on a winning streak? How does it affect the campaign? Does it give Clinton a stronger hand? The answers that came back showed a party struggling to figure out exactly how to deal with the Democrats’ recent run.

Some stressed that the president’s wins aren’t really his, pointing especially to the trade deal, in which Obama succeeded almost entirely because of Republican help.

“Yes, he can claim some victories, but few of his own making and mostly due to other actors, for their own reasons, making things happen,” said Dave Carney, the New Hampshire-based strategist who advised Rick Perry in the last election. “He has become the Forrest Gump of presidents.”

Others laid blame on GOP lawmakers in Congress, arguing they must do more to stop the president’s agenda. “Republicans in Washington need to act and put pressure on Obama to veto conservative legislation or come to the table,” said Tim Miller of the Jeb Bush campaign. “There has been a lot of talking, but Republicans need to start getting results.”

Still others argued that Obama’s wins don’t say much about the merits of his agenda. “He won the (Obamacare) case, but just having the Court say it was legal doesn’t make it good policy, popular with the American people, or good healthcare,” noted Curt Anderson, a top adviser to the Bobby Jindal campaign.

Some saw Obama’s wins as tangential to the issues that matter most with voters, explaining that Obama is still a loser when it comes to the big stuff.

“When the voters start giving the president credit for a booming economy and a globe-spanning string of foreign policy successes, then the Republicans will have to worry,” said Vin Weber, a longtime GOP strategist who is an outside adviser to the Bush campaign.

Finally, others saw Obama’s wins as mainly the work of a Washington establishment out of touch with economic suffering going on beyond the Beltway.

“President Obama and America’s elites are winning, winning, winning,” said Alex Castellanos, a longtime GOP strategist who is not affiliated with any campaign this time around. “Let the peasants eat cake, Obamacare, and unemployment. A lot of steam is building up in the populist pressure cooker. In 2016, some very angry peasants are going to storm Washington with torches and pitchforks.”

One could spend a long time searching those statements for a single, fully coherent strategy to counter the president and neutralize the benefit his victories might confer on Hillary Clinton. That’s not really a surprise, given that there are currently 13 declared candidates, with three more likely to come, in the race for the Republican nomination. But whichever course they choose, Republicans will have to connect with the people who lose when Obama wins.

After the Supreme Court decision, the GOP candidates themselves issued mostly boilerplate statements. They pledged to keep fighting. They vowed, as Texas Sen. Ted Cruz said, to make the 2016 election “a national referendum on repealing Obamacare.” They promised to replace Obamacare with something better.

But what’s going on now is bigger than simply Obamacare. The president is on a roll at the moment, and the Democrat who hopes to follow him to the White House is looking to roll along. Republicans need a focused strategy to stop that momentum. So far, the GOP is still looking.

Byron York is chief political correspondent for The Washington Examiner.