Earlier this week, the US asked for a return of financial aid – about $50 million - while Israel announced it would slap sanctions on the the Palestinian Authority, including a freeze of tax returns and travel restrictions on Hamas officials in Gaza and the West Bank.
On Wednesday, Gaza's al-Mintar (Karni) commercial crossing was closed.
Such moves could prove devastating for the Palestinian economy, which is heavily dependent on the to and fro flux of goods and money.
Atif Udwan, one of five Hamas candidates who swept the northern Gaza district of Bait Hanun, says his group is unfazed by the pressure, arguing these will "only strengthen us".
"We do not wish to foment the world against the new government nor the West. Up to this point we didn’t have an opportunity to show this new face to the West - the real face of Muslims," said Udwan, a professor of political science in Gaza's Islamic University who speaks fluent English.
"History talks about trade cooperation and exchange of cultures."
While Hamas seems optimistic about external pressures, it may have a much more daunting task ahead as it tries to maintain law and order among disenfranchised Palestinian factions.
Near Udwan's home, the Fatah offshoot al-Aqsa Martyrs Brigades, which is responsible for a spate of kidnappings in recent months and a volley of rocket attacks against Israel, have seized hundreds of apartments belonging to the Ministry of Housing.
An elderly man, who worked as a doorman at the housing compounds, and who tried in vain to seek police intervention, complains about the seizure.
The al-Aqsa Martyrs Brigades
could challenge Hamas control
"This is why I voted for Hamas. To stop this madness," says Ibrahim Abo Odeh, 55.
"They [al-Aqsa Martyrs Brigades] are going to be the main obstacles in Hamas's way - not Israel, not the US."
At the apartment buildings, it is the al-Aqsa Martyrs fighters who enforce the law.
They stand guard on the rooftops and balconies of all 280 of their newly acquired flats, just as a police car dismissively patrols the area.
The fighters believe they are entitled to these apartments because they have sacrificed for the Palestinian cause.
"I was shot five times by the Israelis. I've been renting for years now. So tell me-why shouldn't I get a flat of my own?" asks Jamal Durra, 22, a junior member of the Al-Aqsa Brigades.
"Under Fatah, I was getting 500 shekels ($106) a month. Now under Hamas's reign that's stopped, the borders are tightening, and the economic situation will only get worse," chimes in Brigade member Rami Balawi, 22, who shuttles back and forth between his post on the rooftop and a crowd that has gathered below.
"I want to ask Hamas one question: Who will protect me?" says Balawi, nervously clutching the Kalashnikov that is slung over his shoulder.
Addressing such concerns may prove to be Hamas's most immediate challenges.
How Hamas reins in the various dissenting factions who are loyal to Fatah will prove tricky in the days and weeks ahead.
Ahmed al-Kurd, Hamas-elected head of the Dair al-Balah municipality, says the lack of security is hindering reconstruction efforts of areas affected by Israeli home demolitions and bombardments since the Intifada broke out in 2000.
He recently spotted armed men looting and pillaging greenhouses bought for Palestinian farmers in the abandoned Gush Katif settlements.
Dahlan is expected to attempt
takeover leadership of Fatah
The looting began when men from a militia hired to protect the greenhouses abandoned their posts early this month because they had not been paid.
"I called the police and after taking a look they said there was nothing they could do because the people vandalising were members of [Fatah leader Muhammad] Dahlan's preventive security."
Udwan believes strongman and one time security chief Dahlan could pose a challenge as he tries to assume leadership of Fatah and undermine Hamas.
"His moves are quite dangerous. He is trying to make trouble inside the Palestinian community. He provokes and pushes his followers to violence, but we fought against Israel, and believe me, he is weaker than Israel."
From the ground up
Al-Kurd believes Palestinians need to rebuild their civil institutions from the ground up to include the participation of all sectors of society.
But he admitted Hamas was at a quandary when it came to resistance groups outside its control.
Udwan suggests that the problem of the bloated security forces and renegade armed factions can be resolved by placing them under one army, loyal to one government, and one national interest.
"Their loyalty should be to protecting Palestinian security interests. Our policy would be stronger for the next government if we reached some sort of patriotic understanding."
But young Fatah member Balawi, self-appointed spokesperson for the brigade, is not convinced.
"So long as Hamas is in it, there is no unity," he says.
Still, he does not rule out participation in a national army, contingent upon the makeup of this army, and on "guarantees".
By "guarantees", of course, Balawi means money.
Funding security forces
Funding for Fatah security forces comes from the Ministry of Social Affairs, but with recent sanctions from the US and Israel, the Palestinian Authority may find itself unable to pay its young cadre.
"Under Fatah, I was getting 500 shekels ($106) a month. Now under Hamas's reign that's stopped, the borders are tightening, and the economic situation will only get worse"
Al-Aqsa Martyrs Brigades
"We deserve this money. They must also be able to keep the borders open," Balawi retorts.
Balawi's senior, 35-year-old Ahmed Husein, believes ideological differences between the PA and Hamas are a major stumbling block.
He says Hamas's political programme is to reject recognition of Israel as a state which he believes will only harm Palestinian interests.
"If it does not recognise Israel, how will we negotiate prisoner release and keep the borders open? And the Israelis won't negotiate without something return. And if Hamas agrees to give that something in return, they'll have gone against the very platform on which they were elected," he says.
"Either way it's a losing game."