(CNN) Brexit refers to the referendum the U.K. holds on Thursday to determine whether the country will remain in the 28-member European Union. The British debate has largely revolved around economics, sovereignty, immigration and national identity. As the battle rages and polls show the outcome too close to call, here is a look at what it could mean for the U.S. if the U.K. votes to exit the EU:

What does Obama think about Brexit?

While American officials have consistently said the vote is a decision for the British people to make, one of the most visible proponents for the U.K.'s continued membership has been President Barack Obama.

Speaking alongside British Prime Minister David Cameron in London in April, Obama called the referendum "a matter of deep interest to the United States because it affects our prospects as well. The United States wants a strong United Kingdom as a partner. And the United Kingdom is at its best when it's helping to lead a strong Europe."

But U.S. officials have also stressed that whatever the result of the vote, it will not change U.S.-U.K. relations. State Department spokesman John Kirby said last week, "We don't anticipate anything changing the special relationship that we have with the U.K."

Obama's view is not universally held among U.S. politicians. Three Republican senators wrote a letter to the President Monday saying they were "disturbed" by his "seeking to pressure" the U.K.

Sens. Ted Cruz, Mike Lee and Jeff Sessions wrote they think the U.S. should take no official position and that they will await the result of the referendum, but added that the vote "may open new opportunities for cooperation for our British friends and allies."

Why does the U.S. want the U.K. to stay in?

Americans who favor Britain remaining in the EU believe that having one of America's closest allies in the organization aligns the EU more closely with U.S. foreign policy objectives.

During his press conference in London, Obama said, "Americans want Britain's influence to grow, including within Europe."

"Because Britain's values and institutions are so strong and so sound, we want to make sure that that influence is heard, that it's felt, that it influences how other countries think about critical issues," he added.

The Atlantic Council's Frances Burwell, an EU expert who supports the U.K. remaining in the organization, points to the EU slapping sanctions on Iran for its nuclear program and on Russia for Moscow's annexation of Crimea as evidence that the U.K. has helped move the EU toward shared U.S. foreign policy objectives.

What does it mean for the fight against terrorism?

The U.K. and the U.S. have long had one of the world's closest intelligence-sharing relationships, dating back to World War II, and some officials believe that this allows the U.K. to play a critical role in boosting counterterrorism operations in Europe.

Rob Wainwright, director of the European Police Agency, or Europol, told CNN's Clarissa Ward this month that Europe's security is strengthened by this strong U.S.-U.K. intelligence relationship.

"I think the threat that we face from terrorism and, indeed, many forms of international crime at the moment, are much more threatening and complex than we've seen at any point in the past," Wainwright said. "It requires Britain and, indeed, its European partners to enjoy the maximum possible cooperation, making use of course of their unique relationship with the Americans and in the intelligence community."

But appearing on the same program, Michael Howard, a "leave" supporter and former UK home secretary, said that cooperation on law enforcement and intelligence issues with Europe would continue even if the U.K. were to depart the EU.

"They're not so stupid as to cut off their nose to spite their face, just because we decide to leave the formal arrangements of the European Union," he said.

Britain and the U.S. also are both members of NATO, and most experts agree that Britain quitting the EU would likely have little impact since both sides on Brexit support continued U.K. membership in NATO.

Retired U.K. Army Col. Richard Kemp, a Brexit backer who commanded British forces in Afghanistan in 2003, told CNN that because the U.K. spends more on defense that any other EU member, a U.K. exit would prevent the EU from establishing its own military organization that could compete with NATO for limited defense resources among cash-strapped European countries.

if the EU begins to become unraveled, there "can't help but be a knock-on effect for the NATO alliance." But the commander of the U.S. Army in Europe, Lt. Gen. Ben Hodges, warned on the BBC thatif the EU begins to become unraveled, there "can't help but be a knock-on effect for the NATO alliance."

Could it hurt the US economy?

Yes. While the International Monetary Fund released a report Friday that found leaving the EU would primarily hurt the U.K. economy, it could affect the U.S., too -- particularly if there's a significant negative market reaction.

Federal Reserve chairwoman Janet Yellen said last week that the vote "could have consequences for economic and financial conditions in global financial markets. If it does so, it could have consequences in turn for the U.S. economic outlook."

She added that the risk associated with Brexit factored into the Fed's recent decision to not raise interest rates.

How would it impact trade?

Britain is the U.S.'s seventh-largest trading partner. Brexit's affect on that commerce would depend largely on whether America signs a free trade deal with the UK or with the EU.

Advocates of Britain leaving the UK have signaled that such a U.S.-UK deal would be possible. But during his April press conference, Obama said that his priority was negotiating the deal with the EU.

Were the U.K. to exit the EU, Obama continued, "maybe some point down the line, there might be a U.K.-U.S. trade agreement, but it's not going to happen anytime soon."

"The U.K. is going to be in the back of the queue," the President said.

But the prospects for U.S.-EU deal, known as the Transatlantic Trade and Investment Pact (TTIP), are not looking particularly good, as the deal has been slammed by politicians on both sides of the Atlantic.

Britain's exit from the EU could make TTIP even less likely, perhaps giving a boost to the U.S.-U.K. trade deal.

However, Jeffrey Rathke, a former U.S. State Department official, said the current political climate in the U.S. might be hostile to any potential trade deal and he noted that while a UK deal "might not be at the back of the queue, that doesn't matter if the queue isn't moving."

What have Donald Trump and Hillary Clinton said?

Trump, who has expressed some support for Britain leaving the EU, said in May that the UK wouldn't be hurt "at all" in terms of trade negotiations with the U.S. if it exited the EU.