There is one group of people with an even greater interest than Democrats in President Obama prevailing over Tea Party Republicans in this shutdown showdown, and that is mainstream Republicans.

What exactly are supposedly mainstream conservatives — starting with House Speaker John Boehner and Senate Minority Leader Mitch McConnell — thinking? If the “Ted Cruz Wing” of the G.O.P. prevails and forces the president to curtail Obamacare in any way in return for funding the government, mainstream conservatives will be staring at a terrible future. In the near term, they’ll be taking orders from Senator Ted Cruz, who would be crowned kingmaker of the G.O.P. if he got Obama to give in one iota on Obamacare. Cruz and his Tea Party allies would be calling the shots, and Boehner would become that very rare bird — a SPINO (a Speaker in Name Only).

In the long run, because this fringe would be dictating the party line, Republicans would stand zero chance of winning the White House in 2016. If the country rejected Mitt Romney’s bad imitation of a far-right conservative — one hostile to immigration reform, health care, gay marriage and a grand bargain — imagine how the real thing would fare.

Finally, given the way the Republicans have managed to gerrymander so many Congressional districts in their favor, they can easily retain control of the House under any normal economic conditions. But if they trigger a U.S. government default, a disruption in Social Security payments and economic turmoil in their effort to scuttle Obamacare — and a majority of voters blame Republicans — that could overwhelm the G.O.P.’s gerrymandered House advantage.

In other words, the only thing standing between mainstream Republicans and a hellish future of kowtowing to Ted Cruz, never seeing the inside of the White House and possibly losing the House is President Obama’s refusal to give in to the shutdown blackmail that Cruz & Co. have cooked up. The more pragmatic Republicans, who know that this is a disaster for their party but won’t confront Cruz & Co., have settled on this bogus line: “Well, sure, maybe Cruz and the Tea Party went too far, but it’s still President Obama’s fault. He’s president. He should negotiate with them. He needs to lead.”President Obama is leading. He is protecting the very rules that are the foundation of any healthy democracy. He is leading by not giving in to this blackmail, because if he did he would undermine the principle of majority rule that is the bedrock of our democracy. That system guarantees the minority the right to be heard and to run for office and become the majority, but it also ensures that once voters have spoken, and their representatives have voted — and, if legally challenged, the Supreme Court has also ruled in their favor — the majority decision holds sway. A minority of a minority, which has lost every democratic means to secure its agenda, has no right to now threaten to tank our economy if its demands are not met. If we do not preserve this system, nothing will ever be settled again in American politics. There would be nothing to prevent a future Democratic Congress from using the exact same blackmail to try to overturn a law enacted by their Republican rivals.

The president has said that he would give the G.O.P. an agenda for negotiations that could start when the government is funded and the debt ceiling lifted. He’s ready to consider trading the medical-device tax in Obamacare for another equivalent source of revenue or having a talk about closing tax loopholes and reforming entitlements — to both lower the deficit and raise revenue to invest in infrastructure or early childhood education. What Obama will not do, and must not do, is pay an entry fee to that negotiation — say giving up the medical-device tax — just to help Boehner down from the tree. Cruz & Co. would claim victory.

The reason so many mainstream Republican lawmakers want Obama to give something to Cruz & Co. is that they want to get out of this mess, but they’re all afraid to stand up to the far-right fringe themselves — with its bullying network of barking talk-show hosts and moneymen. But Obama shouldn’t take them off the hook. Only Republicans can delegitimize the nihilistic madness at the base of their party. (I wouldn’t exaggerate this, but I think Boehner underestimates how many mainstream Republicans feel their party is being stolen from them by radicals — and hunger for a leader who will take them on.)For their party’s sake and the country’s sake, Republicans need to go through the same kind of civil war and fundamental rethinking that the British Labour Party went through — after successive defeats by Margaret Thatcher — to produce “New Labour” and that Democrats went through — after successive defeats by Ronald Reagan — to produce “Clinton Democrats.”Yes, it will cost them today, but it will enable them to thrive in the future. America needs a proper right-of-center conservative party to challenge a left-of-center Democratic Party. Without a healthy opposition party — one that is ready to win some and lose some and learn from its losses, one that has a real agenda for upward mobility, not just a low-tax obsession and boiling anger — our two-party system doesn’t work, and neither does the country.