And the way his supporters have gone about it has not been entirely peaceful. They have called for Yingluck's overthrow from the occupied halls of seized government offices. They burst through the gates of Thailand's army headquarters and urged the military to "take a stand." And since the weekend, they have tried to battle their way into the prime minister's office with slingshots and burning Molotov cocktails, and threatened to overrun television stations that do not broadcast their message.
Thailand has endured 18 successful or attempted military coups since the 1930s, but so far the army has remained neutral.
Yingluck said Monday she will do everything she can "to bring peace back to the Thai people," but said there is no way the government could meet Suthep's demand under the constitution. Suthep has said Yingluck's resignation and new elections would not be enough.
Thitinan Pongsudhirak, director of Chulalongkorn's Institute of Security and International Studies, said the two sides "believe in different versions of democracy."
"It is a fight for the soul of the nation, for the future of the country," he said. One side wants "to be heard" while the protesters "want the kind of legitimacy that stems from moral authority. Their feeling is ... if the elected majority represents the will of the corrupt, it's not going to work."
The unrest already may have weakened Southeast Asia's second-largest economy. Thailand is a lucrative manufacturing hub whose factories produce everything from computer hard drives to cars that feed a global supply chain. The country is one of the world's leading rice exporters. Its sapphire-blue water beaches are among the world's most popular tourist destinations, but the government has said protests are driving tourists away.
The latest unrest began last month, after Yingluck's ruling Pheu Thai Party tried to ram the controversial amnesty bill through. Even many traditional Thaksin supporters disliked it because it also would have pardoned top opposition leaders.
The bill failed to pass Parliament's upper house, and emboldened protesters drew 100,000 people to a mass rally in Bangkok on Nov. 24. Over the week that followed, demonstrators seized the Finance Ministry and part of a sprawling government office complex that includes the Constitutional Court. They also massed outside half a dozen other government ministries, taking over offices and prompting the evacuation of civil servants some of whom had eagerly waved them inside.
The conflict escalated dramatically this weekend, and blood spilled for the first time. At least three people were killed when anti-government demonstrators clashed with pro-Thaksin "red shirt" activists near a stadium where a pro-government rally was being held.
Outside Yingluck's office at the now heavily fortified Government House, masked mobs launched repeated bids to storm rings of concrete barriers. The police used force there for the first time, unleashing volleys of rubber bullets and tear gas.
The protests have failed to dislodge the government so far, but it remains possible that Thailand's history will repeat itself.
The army deposed Thaksin in a 2006 coup. Controversial court rulings that critics labeled "judicial coups" forced the resignation of two Thaksin-allied prime ministers who followed. One of them was Thaksin's brother-in-law, who saw his own office at Government House occupied by protesters for three months in 2008.
The opposition Democrat Party took over, and in 2009, pro-Thaksin protesters overran a regional summit, forcing heads of state to be hastily evacuated by helicopter from a hotel rooftop. The next year, red shirts occupied Bangkok's glitziest shopping district for weeks in a standoff that ended with parts of the city in flames. More than 90 people died, many of them protesters gunned down in an army crackdown ordered by Suthep, who was deputy prime minister at the time.
The Democrats, who have not won a national election in more than 20 years, were soundly beaten by Pheu Thai and Yingluck in 2011. Protesters claim her ascent was only made possible with Thaksin money.
"You can't call this a democracy," said Sombat Benjasirimongkol, a demonstrator who stood outside a police compound this week. "This government is a dictatorship that came to power by buying votes. Yingluck's supporters are poor. They are uneducated. And they are easily bought."
Pavin Chachavalpongpun, an associate professor at Kyoto University's Center for Southeast Asian Studies, said such claims form a pretext that Thaksin's opponents are using in an attempt to seize power.
The anti-government protest movement is simply "a minority that is refusing to play the game of electoral politics. They cannot compete with Thaksin, they cannot win elections. So they come up with this discourse of village people being so uneducated they don't know how to vote," Pavin said. "But the reality is, these people (Thaksin supporters) are not stupid. They are politically conscious. They have become awakened."
Even if the Shinawatra clan can claim electoral legitimacy, the conflict between the two sides is not black and white.
Thaksin, a billionaire who made his fortune in telecommunications during Thailand's late 80s-early 90s boom years, was accused of manipulating government policies to benefit his business empire. His critics charged he was arrogant and intolerant of the press; at one point he went so far as to have cronies try to buy controlling shares in two influential daily newspapers that had criticized him.
During his five years in office, Thaksin also came under fire for ham-fisted handling of a Muslim insurgency in southern Thailand, and a particularly brutal "war on drugs" that left 2,300 people dead in 2003. Human rights groups complained police were turned loose to kill drug dealers and users at will.
Nevertheless, Thaksin remains hugely popular in Thailand's rural north and northeast and among many of Bangkok's working class for populist polices including subsidized housing and nearly free health care.
Opponents dismiss Yingluck as Thaksin's puppet, though for most of her administration she has trod a more careful path than her brother, building a fragile detente with the army and managing to keep a lid on the nation's divisions. But she was damaged by the amnesty bill, by a court ruling rejecting her party's attempts to boost its power in the Senate, and by controversial policies including a rice-buying scheme that the International Monetary Fund has criticized.
Suthep told The Associated Press recently that his supporters "feel that if the country continues on this path, it will fall into pieces. ... So they come out today to fight for their country and for their children's future."
But Suthep's tactics and his demands have riled even some of his own backers. Democrat lawmaker Korn Chatikavanij, a former finance minister, asked last week: "How will this so-called 'people's government' happen? I still can't quite imagine."
Thailand's political tensions have played out against a backdrop over fears about the future of its monarchy. Thaksin's critics have accused him of disrespecting ailing King Bhumibol Adulyadej and trying to gain influence with Crown Prince Maha Vajiralongkorn, the heir to the throne.
Many hope the conflict will ease Thursday, when Bhumibol turns 86.
The fear is that any peace will only be temporary.
