Mr. Obama has a new mission this year—to make the country believe in political reincarnations. The man who presided over one of the most liberal, most expensive, most government-centric agendas in modern history? It would appear he was kidnapped over Christmas break and replaced by one who is fiscally responsible, a cheerleader for capitalism, and a skeptic of government. It can happen, you know.

As shape-shifting masters like Bill Clinton or Tony Blair might attest, the goal of any move to the center is always two-fold. The first is to lull the public into forgetting past transgressions, and to present them instead with a politician in tune with the pulse of the nation. The second goal—just as important—is to co-opt the other side’s message.

After its midterm victory, the new House leadership crafted a playbook that Majority Leader Eric Cantor unveiled in a briefing in the first days of January. Week one the Republicans would devote to repealing ObamaCare. Week two would focus on the party’s plans to roll back discretionary spending to 2008 levels. Week three would laser in on the president’s job-killing regulatory blowout.

The White House was listening and has been hustling to get ahead of the GOP message machine. Nowhere was this more obvious than in the president’s Tuesday op-ed on this editorial page announcing an executive order to restore “balance” to federal regulation and root out rules that hurt economic growth. It was a largely symbolic move, designed to counteract the public perception that Mr. Obama is antibusiness, and to bolster corporate America’s support.

The exact strategy will be on display in the president’s State of the Union address on Tuesday. Next week is GOP Cut-Spending Week, though the Tucson delay means it will now be the president who commands the network cameras. And Mr. Obama will smartly use the hour to highlight his own supposed commitment to fiscal responsibility, to muddy the waters, and to again suggest that any differences between his team and Republicans are minor policy disputes, not a philosophical divide.

Count on Mr. Obama also to use his speech to address his health law. This is tougher for the White House. Republicans have a clear repeal message. The White House approach so far is to argue both sides should work together to find ways to “improve” the law, that repeal is a waste of time, and that the only thing standing in the way of finding common ground will be opportunistic GOP politicking.

Republicans figured that all this might be coming, and the serious ones are, if anything, hopeful about it. Far better, they note, to have a president who may be open to helping the economy than one who isn’t. The great unknown is whether Mr. Obama means any of this, or if it is entirely rhetorical. President Clinton’s own movement, after all, was only successful because he was serious enough about it to craft bipartisan victories like welfare reform.

The Republican opportunity now shifts to finding out. In two years in office, Mr. Obama has proven adept at saying one thing while doing another. The difference now is that control of the House allows the GOP to point out the distinctions. A broad complaint—say, that Mr. Obama is “pro-regulation”—may not work. But the GOP does have the ability to send, week after week, clear pieces of legislation to the Senate that will challenge Mr. Obama to back up his rhetoric with action.

A first example: Republicans are unveiling a bill to prohibit taxpayer-funded abortions. Mr. Obama claims to believe in this; last year he signed an executive order that in theory backs the ban. The GOP legislation would codify the prohibition. Will the president demand the Senate take a vote? The president may be hoping that Senate Majority Leader Harry Reid will shield him from some of these legislative challenges. But Republicans intend to make Mr. Reid’s intransigence a daily issue and in the process put Mr. Obama on the spot.

The White House is making new promises. For its own sake, it had better mean some of them. The president skated through the first part of his term with Washington in awe. Circumstances have changed. The administration may be shrewdly co-opting GOP talking points, but the GOP today has recourse. And it could be that a president who claims to be something he isn’t is as much a problem for voters as a president with a misguided agenda.

Write to kim@wsj.com