Jon MacKay is an affiliate researcher of the Waterloo Institute for Complexity and Innovation. William Bendix is assistant professor of political science at Keene State College, in New Hampshire.

Ever since Obamacare became law, Republicans have loudly and consistently claimed to hate it. Yet even Donald Trump, the dealmaker-in-chief, failed to rally enough support to repeal and replace Obamacare. The President blames the failure on the Democrats.

The real problem is that the Republican Party is plagued by partisan infighting. Mr. Trump was able to use the ideological differences between factions in the party to his advantage during the election campaign. Not only did he overthrow the party's traditional leadership, he united many of the other competing interests in the party.

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But the campaign is over now. The factions in Congress are starting to make the President's life much more difficult. What's the basis of Republican disunity? Aren't Republicans, whether elites or voters, all staunch conservatives who oppose the Democrats? Yes, but as our research shows, it isn't quite that simple.

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We examined how several hundred interest groups have rated congressional Republicans since 2001. We found three distinct factions that were stable over time. Each represented different sets of ideological interests. The party leaders reside in what we call the corporate-establishment faction – a group that advances pro-business policies. The difficulty is that two other Republican factions also compete for power: a lunch-pail faction, whose members focus on working-class issues, and an ethno-radical faction, whose members support a mix of nativist and fiscally regressive policies.

What's become clear is that any policy decision he makes is now likely to produce as many losers as winners within their party's coalition.

After the health-care defeat, Mr. Trump has said he'll next turn to tax cuts, dramatically lowering taxes across the board. His plan, estimated to reduce federal revenues by $6-trillion (U.S.) over ten years, will provide much greater tax relief to the affluent than it will to middle- and working-class voters. This makes it, in many respects, a mainstream Republican proposal.

But that's the problem. Massive revenue cuts need to be offset by large spending cuts, otherwise the national debt will balloon. Mr. Trump wants to boost military spending, cut taxes and slash industry oversight and entitlement programs. That likely suits the corporate establishment and the ethno-radicals of the party, but it will outrage most everyone else – including lunch-pail voters. True, Trump could cut taxes and increase spending without totally blowing up the budget by issuing 100-year bonds. But it's hard to imagine the ethno-radicals supporting this big-government, big-debt strategy.

Trade protectionism, another pillar of Mr. Trump's election campaign, is the most important issue for Canada. Although famously inconsistent on many issues, Trump has been unwavering on trade. He has already abandoned the Trans-Pacific Partnership and has said that he wants to reopen NAFTA, impose tariffs on individual firms, and possibly withdraw the U.S. from the World Trade Organization.

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These promises are aimed at lunch-pail Republicans, who have seen manufacturing jobs disappear over the last three decades. But this anti-trade agenda is at odds with the corporate establishment of the party – which has, since at least Ronald Reagan, advocated trade liberalization.

In Canada, the federal Liberals are doing the right thing in trying to engage those U.S. states we trade most heavily with. However, understanding the factional constraints on the President will be useful in renegotiating our own free-trade deal with America – a priority rising rapidly on the President's agenda.

Altogether, these examples show that Mr. Trump's plans and Republican priorities are contradictory, if not incoherent. He can't set a unifying agenda for his party because, as soon as he decides to serve one faction, he'll inevitably disadvantage another. Things will fall apart, probably sooner rather than later.

Is there a way for Mr. Trump to minimize bitter partisan infighting? We expect that he'll continue to rely on the force of his rhetoric and personality to divert attention away from internal Republican divisions. He'll continue to attack outsiders and opponents as he struggles to keep his coalition intact. Demonize Mexicans and Muslims. Rail against international organizations. Threaten trading partners. And blame the Democrats for any stalled legislation.

This kind of scapegoating may work initially, but it's hardly a long-term governing strategy. At some point, one of the Republican factions, disappointed by the almost certain policy losses, will surely abandon him. The question is, which one will leave first and how will Mr. Trump respond?