It’s right to view the Tea Party’s members and fellow travelers as fixated on domestic politics and policy. But it’s wrong to reckon that they will fail to have a serious and invariably disruptive impact on future foreign policy. Indeed, their power is likely to grow, despite their defeats in October over the federal budget and the debt ceiling. Their sway will mount because they still face little effective opposition from within the Republican Party in most parts of the nation. And there is little doubt about the damage they can and will inflict: They will threaten what remains of the Republican Party’s great tradition of internationalism and further strain the ability of any U.S. President to conduct diplomacy, to negotiate, and to compromise. To Tea Party members, these three staples of a successful foreign policy are akin to unilateral disarmament.

Republican and Democratic internationalists should not console themselves because of the apparent divisions among Tea Partiers over foreign policy—the seeming divide between unashamed isolationists like Rand Paul and unabashed hawks such as Ted Cruz. It would be wrong to bet on those differences marginalizing the movement’s impact. More likely, the Tea Party’s varying messages will fuse into a reborn and more potent form of hawkish isolationism.

This fusion will be reminiscent of Barry Goldwater’s brief triumph over Nelson Rockefeller in the race for the 1964 GOP presidential nomination, during which Goldwater warned against foreign entanglements, but applauded General Curtis LeMay’s nuclear “bombs away” prescription. After Goldwater, the traditional Republican thread reasserted itself for more than two decades, led by Richard Nixon, Henry Kissinger, George H.W. Bush, James Baker, George Shultz, and Brent Scowcroft. Their realist policies and shrewd agreements with adversaries defined Republicanism abroad.

The new hawkish isolationism, however, will reassert itself in the 2014 congressional races and in the 2016 Republican presidential primaries. The Tea Partiers proved their power in earlier elections when they toppled conservatives like Utah’s Bob Bennett and Indiana’s Richard Lugar. The latter represented Republican internationalist realism, and his defeat was devastating, symbolically and practically. The Tea Partiers are now gunning for others formerly considered conservative stalwarts, such as Mitch McConnell, Lindsey Graham, Lamar Alexander, and Thad Cochran, four senators rightly seen as at least semi-internationalists.

The fight to retire those four is just the beginning. Heritage Action—the political arm of the Heritage Foundation run by former Republican Senator Jim DeMint—recently had its best-ever fundraising month. Sitting on that cash is not in the cards. And as increasing numbers of Republican officeholders face defeat because Tea Partiers deem them RINOs—“Republicans in Name Only”—it is probable that traditional conservatives under attack will seek a form of cheap grace. If they continue to oppose fiscal hostage-taking, they will likely attempt to “get well” with the Tea Party by endorsing its opposition to free trade, immigration reform, and attempts to resolve disputes involving Iran, Syria, and China with diplomacy.

Tea Party isolationism is just a somewhat new variant of the old Robert Taft position. On the surface, there is the Marco Rubio/Ted Cruz wing that wants increased defense spending and tough, if ill-defined, action against Iran and China. They sound something like neoconservatives. The Rand Paul libertarian wing talks much more like traditional isolationists. They want a near-total focus on domestic issues without any global distractions.

But look beyond such headline rhetoric and a common thread emerges: a Tea Party-wide reluctance to engage with the world, except for those they view as true U.S. friends, such as Israel.

Like most Americans exhausted by too many inconclusive foreign military engagements, the Tea Party flees from the thought of a ground war in Syria. But they wouldn’t mind clobbering enemies there if they could get them from afar (although some, like Sarah Palin, would gladly sit by and “Let Allah sort it out”). For many Tea Partiers, an outsized defense budget is not meant as a prelude to military intervention; rather, it is their unrealistic way of keeping threats as far from America’s shores as possible.

Count on three consequences then. First, a stronger, even more vociferous Tea Party. Second, a growing isolationist, anti-world impulse among its adherents. Third, much rougher opposition for any President wanting to conduct necessary business abroad.

In today’s world, Presidents must work with and through international institutions. Tea Partiers distrust every one of them (especially the United Nations) as they rail against any “loss” of national sovereignty.

There is no doubt that the Tea Party is going to make international negotiations difficult. Anything that requires give and take—such as forging decent working relations with China—will face hostility from those who won’t tolerate any give at all. In fact, some, like Senator Rand Paul, have talked only about the “take”—threatening a trade war with China in the quixotic hope that such a stance will cause Beijing to pressure nations like North Korea to bend to U.S. wishes.

Perhaps the most vexing problem facing the West involves Iran’s nuclear ambitions. The chance to improve relations with Tehran, a potentially monumental event of Cold War-ending proportions, will require the Obama Administration to offer proposals that not only protect American interests but are acceptable to Iran as well. That will mean reducing, and over time ending, the sanctions that are crippling Iran’s economy. But in many instances, rolling back sanctions will require congressional approval, which will require House acquiescence, which in turn will require Tea Party assent. And that is just not likely, especially if Israel continues to oppose any serious diminution of economic pressure. As the elements of a possible deal with Iran become clearer, Marco Rubio’s position, which is likely shared by other Tea Party leaders, is virtually indistinguishable from Israel’s. Rubio has said he will support lifting sanctions only if Iran agrees to “completely abandon any capability for enrichment or reprocessing” of nuclear materials. This is a nonstarter for Tehran, since it would require nothing less than Iran’s total capitulation.

It is already extremely hard for any U.S. President, especially a Democrat, to make deals with presumed devils. Richard Nixon may have established a new working relationship with China and Ronald Reagan negotiated far-reaching arms control agreements with the Soviet Union. But neither accomplishment would have happened without the active support of both Republican and Democratic internationalists. If the Tea Party continues to extend its sway over congressional Republicans—and it remains to be seen if a plausible countertrend can succeed—the ability of Barack Obama to embrace the essential compromises of diplomacy could face an insurmountable wall.