Many hurdles for new UK government

STORY HIGHLIGHTS

Zakaria: UK coalition may work because parties are "reasonably close." can compromise
Two "hot-button" issues the parties are strongly divided on are the EU and immigration
Zakaria says "Britain will remain America's closest ally"
He says new government will have to make painful budget cuts and tax increases

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Editor's note: Fareed Zakaria is an author and foreign affairs analyst who hosts "Fareed Zakaria GPS" on CNN U.S. on Sundays at 10 a.m. and 1 p.m. ET and CNN International at 2 and 10 p.m. Central European Time / 5 p.m. Abu Dhabi / 9 p.m. Hong Kong.

London, England (CNN) -- Gordon Brown resigned as British prime minister Tuesday, paving the way for David Cameron to replace him.

Brown announced his intention outside 10 Downing Street -- the prime ministerial residence -- before being driven to Buckingham Palace where he formally handed his resignation to the queen.

About one hour after Brown's resignation, Cameron -- leader of the right-wing Conservative Party -- became prime minister.

The Conservatives won the largest number of seats, but not enough to let them govern on their own. Brown's left-wing Labour Party came in second, and the Liberal Democrats third.

Zakaria told CNN that a coalition government between British Liberals and Conservatives could work in many ways, but the parties will remain divided on issues such as the European Union and immigration. Zakaria also feels that Britain's new government will have to make painful budget cuts and tax increases.

Zakaria, author and host of CNN's "Fareed Zakaria GPS," spoke to CNN on Thursday. Here is an edited transcript:

CNN: With so much discontent with the Labor Party and Gordon Brown -- why didn't David Cameron and the Tories win the election outright?

Fareed Zakaria: Many people think it's because David Cameron is not that charismatic. I tend to think the problem is deeper. Conservativism in Britain got associated with nastiness and nuttiness in the 1990s, and it's taking a while to soften that image. The Tory party brand is still somewhat damaged. Now this might well change once people see Conservatives in government and see that they are quite mainstream. Certainly that's what Cameron is trying to do with his very moderate remarks and gestures to liberals. He called his coalition a "Liberal-Conservative" coalition, even though the Conservatives have 306 seats and the Liberals have only 57.

CNN: On a practical level, how effective can a coalition government be?

Fareed Zakaria: We don't know. Britain hasn't had one since World War II and that was obviously under exceptional circumstances. But on many issues, the two parties are reasonably close and can find ways to compromise. Britain's three parties are all, by American standards, mainstream. The entire British political spectrum would fit inside the Democratic Party, with some Tories being a bit to the right of the Democrats -- but substantially to the left of most Republicans. There is no full-throated American-style conservatism in Britain anymore. Or if there is, its members are hiding. On gun control, nationalized health care, welfare, regulation, the Tories are closer to Democrats than Republicans.

CNN: What about issues such as the EU and immigration? Do you think the Liberal Democrats and the Tories will be able to find common ground on these issues?

Fareed Zakaria: Those are the two areas where there is genuine disagreement. And on both issues, the Conservative position is far more popular. The Liberals are very pro-European -- they want Britain to adopt the Euro. That's a position few people in Britain support -- especially as they watch the Euro go through its troubles right now. On immigration, the Liberals want to give amnesty to illegal immigrants, which in Britain (as in America) is a hot button. So my guess is, in both cases, the Conservatives will prevail because the Liberals won't push for something so unpopular.

CNN: The primary challenge facing the UK is the economy. Is Cameron up for the challenge?

Fareed Zakaria: That's the key question. It's not just the economy. Britain's budgetary position is not quite as bad as Greece, but it's not so far off either. The new government will have to impose a good bit of pain on the society, in the form of budget cuts, tax increases, etc. Is Britain ready for that? To his credit, Cameron did campaign on the idea of sacrifices and pain. But he never outlined the extent of the cuts he would have to make and left vague what, if anything he would cut. Once things get specific, the howls of protest will begin. But Britain's experiments will be important to watch because Britain's present is America's future. We too will have to impose pain on Americans and no politician so far has been willing to talk about it in any detail.

CNN: Will the U.S. relationship with Great Britain change with the new government in London?

Fareed Zakaria: No, Britain will remain America's closest ally. Britain gets enormous advantages from being that close to the world's only superpower. But I think we'll see less Churchillian rhetoric and a more modest stance. Partly this is because Britain is paring back its world role anyway. It is cutting back the Royal Navy and cutting its expeditionary forces. In that context, grand speeches about spreading democracy and opposing evildoers will sound hollow. And Cameron strikes me as much less grandiose in his vision of foreign policy than Blair.