WASHINGTON — President Obama's international woes give his former secretary of state good reason to seek political distance. Hillary Rodham Clinton's recent foreign policy criticisms made that clear.
Domestically, their interests diverge in a different way. A Republican takeover of the Senate this fall would hurt Mr. Obama for the final two years of his presidency, but it might help Mrs. Clinton if she runs to succeed him.
Republican control of both the House and Senate would provide Mrs. Clinton a clearer target to run against in courting voters fatigued by Washington dysfunction. The longer an unpopular president and his more-unpopular partisan adversaries battle to a standstill, the easier to offer herself as a fresh start.
"It would be bad for the country," said Stanley B. Greenberg, President Bill Clinton's former pollster, but "total gridlock would allow Hillary to be the change."
That doesn't mean that Mrs. Clinton, herself a former Democratic senator, would do a single thing to make that happen. Unlike Mr. Obama, she is in demand to campaign for fellow Democrats this fall. She has strong incentives to help them and win friends among voters, elected officials and donors, just as potential Republican foes do for their party's candidates.
Yet it offers another illustration of the ways in which the political paths of Mr. Obama and Mrs. Clinton, after their unlikely four-year partnership, can point in different directions.
For all the strengths she would bring to a 2016 race, Mrs. Clinton would face a significant historical obstacle. American voters have demonstrated their reluctance to award the same political party a third consecutive term in the White House.
The combination of fatigue with the incumbent party and rejuvenation by its opposition helped stymie Richard M. Nixon when he sought to succeed Dwight D. Eisenhower in 1960 and Hubert H. Humphrey when he tried to follow Lyndon B. Johnson eight years later. Al Gore lost in 2000 despite President Clinton's high approval rating and economic record.
In the last 60 years, only George Bush managed to capture a third straight presidential victory for his party. He did it in 1988 — two years after the Democratic opposition had regained unified control of Congress by retaking the Senate in midterm elections.
Congress made trouble for President Ronald Reagan in his last two years by investigating the Iran-contra scandal, overriding his veto of highway legislation and rejecting his Supreme Court nominee Robert H. Bork. In Mr. Bush's winning campaign, however, he used "liberal Democrats" on Capitol Hill as a foil for his "read my lips, no new taxes" pledge at his nominating convention in New Orleans.
If she were the 2016 Democratic nominee, Mrs. Clinton would have a similar opening to deride Tea Party Republicans in the House even if Democrats keep the Senate this November. But all-Republican control of Congress would magnify it.
In part, of course, that depends on what Republicans do in the next two years. Mr. Obama has been frustrated by his inability, even after a decisive 2012 re-election victory, to "break the fever" of hard-core Republican opposition. With control of both chambers of Congress, Republicans might feel a greater responsibility to join Mr. Obama in governance by striking politically appealing compromises.
"If the direction Republicans define is where the country needs to go, then the initiative is with Republicans," said David Winston, a Republican strategist for House leaders. "If Republicans just define themselves as being opposed to President Obama, then Republicans hand the initiative to Clinton."
But evidence from recent years offers little reason to expect that the party will move in a more popular direction. The power of the Republican right has prevented the House, for example, from acting on an immigration overhaul or avoiding a government shutdown despite the express wishes of Speaker John A. Boehner.
Congress as an institution suffers from approval ratings some 30 points lower than Mr. Obama's. The Republican Party fares worse nationally than Democrats — and has almost continuously since the latter years of President George W. Bush's administration.
"A Republican Congress will present an inviting contrast and easily understood negative for whoever runs for president as a Democrat," said Anita Dunn, a former White House communications director for Mr. Obama.
At the same time, she added, "The president will have two more years to get things done and clearly a Democratic Senate would be better for that." As little as Congress is doing now, losing the Senate beachhead poses numerous dangers to Mr. Obama's agenda.
Republicans would control which of his appointees receive confirmation votes, and how quickly. They could, as their House counterparts have done, initiate investigations of the administration.
They could make him use his veto pen to fend off legislation impeding his climate-change initiative or repealing parts of the health care law. They could seek smaller compromises on trade, infrastructure or business taxation on terms that force Mr. Obama to choose between alienating his Democratic base or accomplishing nothing further before leaving office.
Mr. Obama might find solace later if troubles in his closing act end up smoothing the path for Mrs. Clinton. He won landmark victories in his first two years with a Democratic Congress on economic stabilization, health care, financial regulation and budget priorities. Through use of executive authority, he now aims to add to them on his own on climate change and immigration.
In the polarized politics of the early 21st century, the surest guarantee that Mr. Obama's political legacy will endure is easy to see. It is another Democratic presidency.
—By John Harwood, The New York Times