The Republican Party suffered another humiliating defeat at the hands of Barack Obama yesterday. The Republicans essentially got nothing in the deal to end the government shutdown and were barely able to keep the spending caps of the sequestration, one of their few victories, in place.

The past few weeks have seen Republican approval plummet to record lows in several polls including those by Gallup and NBC News/Wall Street Journal. A new Pew poll released Oct. 16 shows that Tea Party support among Republicans has fallen by nine points since June. Independents disapprove of the Tea Party by a 19 point margin. GOP supporters feel betrayed by the deal. Reactions range from anger at “RINOs” or the Tea Party to resignation that the Republican Party is totally ineffective and unworthy of support.

While there is very little upside to the debacle in the short term for Republicans, it does provide them with a few hard lessons to learn. If the GOP can take these lessons to heart, it may eventually save itself and the turn the country around in the process.

Lesson 1. Check your math. The inevitability of defeat in the defund battle could be summed up in the mathematical expression 45<55. Forty-five Republican senators are less than 55 Democratic senators. The Republican will always lose in the Senate unless they can sway Democrats to vote with them. In the defund battle, there was little, if any, effort expended on pressuring red state Democrats to join the Republicans.

It does not matter if the Republicans are standing for principle. It does not matter how courageous they are. In an election, math trumps everything. The only way to win is to change the math. Subtract votes from the Democrats and add them to the Republicans.

Dividing the party into “RINOs” and Tea Partiers is counter-productive. Neither faction can win without the other. Division only subtracts from the Republican votes and gives the Democrats a larger majority.

Lesson 2. Pick your battles. The Republicans are a minority party. They cannot take on the majority party head-to-head and win. Even if every RINO and every Tea Partier is united in the cause, 45 is still less than 55 (see lesson 1.)

Republicans should take a lesson from General George Washington. Rather than wasting time and resources on a head-to-head battle that has no chance of success and will likely destroy their force, Republicans should fight smaller battles when they have a reasonable chance of winning.

In the early days of the American Revolution, Gen. George Washington faced the world’s most powerful army with a ragtag band of militia. Washington did not march his men straight into the British cannons. Rather, he acted to preserve his army and made strategic withdrawals when the conditions were unfavorable. His most famous retreat came in August 1776 during the Battle of Long Island in which a fog that many attribute to divine intervention saved the Continental Army.

Washington picked his battles and attacked when conditions were favorable. A few months later on Christmas Day 1776, he made his famous crossing of the Delaware to surprise the British at Trenton. As Washington grew stronger and received reinforcements from the French, he was able to fight the British more directly. It was only after the Americans outnumbered the British that they were able to surround them and force their surrender at Yorktown.

If the Republicans had chosen to make a stand over congressional exemptions or the mounting federal debt rather than over defunding Obamacare, the results might have been different. While only a slight majority disapproves of Obamacare, a staggering 94 percent of voters in an Independent Women’s Voice poll opposed the exemption. Likewise, 61 percent told Gallup that the federal budget deficit worried them “a great deal.” These are bipartisan issues where the Democrats would be vulnerable to a “flank attack.” The Democrats would be forced to vote with the Republicans or go on record against strong public opinion.

Lesson 3. Pay attention to polls. Polls should not be used to determine your principles, but they are invaluable in determining a strategy. As Examiner reported in September, a poll commissioned by Republican congressmen themselves found that 71 percent of Americans opposed shutting down the government to fight Obamacare. Scores of other polls gave the same warning.

While Republicans claimed to be fighting for what the people wanted, they were instead ignoring the people’s mandate to keep the government opening. As a result, they paid dearly in terms of public approval.

Lesson 4. When your enemy is about to destroy himself, don’t stop him. The rollout of the Obamacare exchanges was an unmitigated disaster. Even worse for the Democrats, high premiums across much of the country challenge the underlying economic assumptions behind the law.

Fortunately for the Democrats, much of the country was distracted by news coverage of the government shutdown. If the Republicans had simply stood by as President Obama’s signature law imploded, they might have improved their chances of winning the Senate in 2014. Instead, generic congressional ballots, which had been tied before the shutdown, uniformly shifted toward the Democrats according to the Real Clear Politics roundup of polls.

Lesson 6. Think long term. The Constitution requires a majority to pass laws. The Republicans are a minority. Therefore, their focus should be on becoming a majority (see Lesson 1.)

Long term Republican success depends on appealing to moderates as well as the party’s base. Gallup’s most recent party identification poll gives Republicans 20 percent and Democrats 30 percent. Forty-seven percent of the electorate is independent. The party makeup in the states is similar. Neither party can win without winning independents. It is these moderate voters who decide elections.

A successful Republican strategy will appeal to both the party’s base and the country’s moderates. A politician or a party that cannot appeal to both the base and moderates is what is known as a loser.

Thinking long term also includes having an endgame or a Plan B. When the initial Republican demand for defunding Obamacare was rejected, the Republicans seemed totally unprepared. The party was trapped with no way out. With approval ratings falling fast, the Democrats could have demanded almost anything to reopen government and the Republicans would have had no choice but to take the deal or let Obama lead the nation into a default for which the GOP would surely take the blame.

It would have been wiser to have positions to fall back to when the initial demand failed. These strategic withdrawals should have been accompanied a common message that focused on what the Democrats were doing to harm the American people, not what other Republicans were doing to harm the party.

Lesson 7. Perception is the political reality. Communication shapes perceptions. President Obama and the Democrats refused to negotiate, but the public perception was that Republicans wanted the shutdown so they took the lion’s share of the blame.

While Republicans dithered and squabbled, Daniel Henninger notes that Team Obama launched a withering assault of tweets to complement friendly news coverage. The Democrats never strayed from their message that “Tea Party Republicans” were threatening to destroy the economy. Without a coordinated response from the Republicans, Obama’s message became the defining story of the shutdown. Republicans must learn to use the social media to counter Democratic propaganda in both the mainstream media and the twitterverse.

By focusing on the long-term and uniting with disaffected moderates against President Obama and the Democrats, the Republicans still have a chance to make a comeback before next year’s midterm elections. A strong showing could change the equation in the Senate (Lesson 1). The structure of the races favors Republican gains in the Senate, but a strategy of tilting at windmills is likely to result in yet another missed opportunity.

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