The Note's Must-Reads are a round-up of today's political headlines and stories from ABC News and the top U.S. newspapers. Posted Monday through Friday right here at www.abcnews.com

Compiled by ABC News' Jayce Henderson, Amanda VanAllen, Carrie Halperin and Will Cantine

PRESIDENT OBAMA / FOREIGN AFFAIRS: ABC News' Jonathan Karl and Devin Dwyer: " White House Suggests Obama Could Meet With Iran's New President" There's nothing on the official schedule, but the White House is sending signals that President Obama is willing to meet with Iran's new president and that the meeting could happen next week when the two leaders will be in New York for the United Nations General Assembly. Any encounter between President Obama and newly elected Iranian President Hassan Rouhani would be historic. No American president has met with an Iranian head of state since Jimmy Carter met with Shah Mohammad Reza Pahlavi in Tehran on New Year's Eve in 1977. The U.S. cut off diplomatic relations with Iran in 1980 after the seizure of the U.S. embassy in Tehran. LINK

USA Today's Aamer Madhani: " Obama Open To Meeting With New Iranian Leader At UN" The biggest moment at next week's meeting of the United Nations General Assembly could be a handshake that may or may not happen. As world leaders prepare to descend on New York for the annual meeting of the world body, all eyes are on what interaction, if any, President Obama and the newly installed Iranian President Hasan Rouhani have at the UNGA. LINK

The Washington Times' Guy Taylor and Ashish Kumar Sen: " Kerry tells U.N. to focus on ridding Syria of chemical weapons, not on sarin attack" Secretary of State John F. Kerry on Thursday urged the U.N. Security Council to ignore Russia's questions about the source of chemical weapons used in the Syrian civil war and to back quickly the plan to rid Syrian President Bashar Assad's regime of its stockpile. Even as Obama administration officials appeared to back down from the U.S.-Russian deal's initial mandate requiring Syria to account for all its chemical weapons by this weekend, Mr. Kerry called on the international body to avoid getting bogged down next week in a debate questioning American evidence about the regime's role in last month's chemical attack on a Damascus suburb. LINK

The Washington Post's Anne Gearan and Jason Rezaian: " Iran's Hassan Rouhani prepares for his debut trip to the United Nations" In the often colorless realm of international diplomacy, one annual ritual has stood out for years - a provocative speech by Iran's leader to the United Nations each September, followed by a walkout by U.S. and Israeli delegates. That bit of diplomatic theater may not happen this year, as a new Iranian president who has alternately pleased, intrigued and startled American observers makes his debut trip to the annual gathering of world leaders in New York. LINK

CONGRESS / GOVERNMENT SHUTDOWN: The Wall Street Journal's Janet Hook and Kristina Peterson: " Spending Battle Set For The Senate" The Senate began girding for a contentious fight over a bill to fund the government after conservatives on Thursday threatened to use delaying tactics in an effort to eliminate money for the new federal health-care law. The vow from Sen. Ted Cruz (R., Texas), a leading foe of the health law, pointed to a protracted and uncertain Senate battle that could drag Congress close to the Oct. 1 deadline for avoiding a partial government shutdown. LINK

The Los Angeles Times' David Lauter and Lisa Mascaro: " Government shutdown is no idle threat" Outside the capital the prospect might seem unthinkable, but inside it seems increasingly likely, and to some inevitable: In less than two weeks, the federal government, from the Agriculture Department to the Weather Service, may shut its doors. Agencies already have contingency plans for stopping all but essential work. Soldiers would be required to report for duty but would not be paid. National parks would be closed and overnight campers would be given two days to leave. Social Security checks would go out, but the agency would stop updating people's earning records. The State Department would stop issuing most passports. LINK

DEBT: Bloomberg's Greg Giroux: " Senate Budget Chief Sees Republican Yield on Debt Lifting" Republicans seeking to curb President Barack Obama's health-care law probably will capitulate to demands from Democrats to enact a "clean" bill raising the nation's debt ceiling, the Senate's top Democratic budget writer said. "I see no deals on the debt ceiling," Senator Patty Murray of Washington state, who leads the Budget Committee, said in an interview on Bloomberg Television's "Political Capital with Al Hunt" airing this weekend. LINK

ENERGY AND THE ENVIRONMENT: Politico's Erika Martinson: " Coal in Obama's climate crosshairs" The Obama administration is preparing to draw a red line against coal pollution, with a proposal that for the first time would limit climate-changing emissions from all future power plants. The Environmental Protection Agency's proposed rule, set to come out Friday morning, fulfills a key promise to President Barack Obama's environmental base - while offering a potent line of attack for Republicans in 2014. It kicks off a major effort by Obama's agencies to tackle climate change without waiting for help from Congress. LINK

FOOD STAMPS: The Hiil's Kevin Bogardus: " House votes to cut food stamps by $39 billion" The House approved legislation Thursday that would cut $39 billion in funds over the next decade for food stamp programs. Members approved H.R. 3102, the Nutrition Reform and Work Opportunity Act, in a close 217-210 vote. No Democrats voted for the bill, and 15 Republicans voted against GOP leaders. LINK

ABC NEWS VIDEO: " Carney Defends Credibility After Assad Claims" LINK

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