President Obama on Tuesday will lead a special summit on the need to take in Syrian refugees, just days after weekend terrorist attacks that are raising more questions about whether the U.S. should be cracking down on immigration instead of opening the doors further.

Plans for Obama to lead the summit were months in the making, long before Ahmad Khan Rahami allegedly planted a pressure cooker bomb in New York that detonated, injuring 29 people. Rahami, a naturalized U.S. citizen born in Afghanistan, is also thought to be responsible for bombs discovered in New Jersey.

The incident puts real pressure on Obama to make the case for taking in thousands of additional refugees, in the face of calls from Donald Trump and other Republican critics who say it's time to tighten the rules, not ease them. Obama's critics say the timing couldn't be worse.

"The timing of the summit just reinforces the idea that we need to get a handle on our refugee program," Rep. Brian Babin, R-Texas, told the Washington Examiner. "There is a clear and present danger posed to our national security by these poorly vetted refugees that are pouring in, and the president continues to double down on his intentions to bring in more and more of the individuals from hot spots like Syria."

Babin last week wrote a letter to Speaker Paul Ryan, R-Wis., urging him to include provisions in the continuing resolution to fund the government that would place a moratorium on refugees coming from terrorist hotbeds in Syria, the Middle East and North Africa. Thirty-seven House GOP colleagues signed onto the letter.

The Texas Republican said his effort to put a halt to the admission of the refugees is even more important after this weekend's terrorist attacks in New York, New Jersey and Minnesota.

"The people of the United States and of Western Europe are getting very weary about the politically correct pressure that is being brought to bear by Obama and the U.N. to take in people," including those that top U.S. national security officials have said we "cannot properly vet."

FBI Director James Comey, Department of Homeland Security Director Jeh Johnson and Director of National Security James Clapper have each testified to Congress over the last year that they couldn't certify that every single refugee admitted into the United States was not a security threat.

Those officials have all testified before several congressional panels about the challenges and information gaps that exist when screening refugees and have emphasized that there is no risk-free process. Comey, however, specifically has said the State Department and other agencies have "dramatically" improved the process over the past few years, and over the past few months, when it comes to Syrian refugees.

Holding Obama's U.N. summit meeting just after the weekend terrorist bombings is also causing headaches for Hillary Clinton, who has called for increasing U.S. admissions of Syrian refugees to 65,000. Her opponent has taken full advantage.

Just hours after the Rahami was arrested, Trump blasted Clinton for supporting policies like the admission of Syrian refugees, which he said would allow radical Islamic groups to "continue their savagery and murder."

The Republican presidential nominee and other GOP critics have also assailed the Obama administration over a new Department of Homeland Security Inspector General report that said the agency mistakenly granted citizenship to at least 858 immigrants from countries deemed to pose security concerns to the U.S.

"We need to get smart and get tough fast so that this weekend's attacks do not become the new normal here as it has in Europe and other parts of the world," Trump said in a statement Monday.

Christian Whiton, a former senior State Department adviser in the George W. Bush administration, said Obama's and Clinton's insistence on pushing for the admission of more Syrian refugees is playing into Trump's hands in the final weeks of the election.

"If you look at polls — only 35 percent of Americans want Syrian refugees to come here — I think they instinctively know that these people cannot be vetted," Whiton said.

After the weekend's bombings and Obama's U.N. summit, he predicted that Clinton would have a very difficult time defending her push for more Syrian refugees on the campaign trail.

"Hillary is pathologically committed to bringing more refugees here, knowing full well that there will be Islamists and jihadists among them," he told the Examiner. "How can she possibly think the government can screen out those who adhere to radical Islam if she won't even name that threat?"

"The twin pillars of Hillary's worldview are globalism and multiculturalism," he said. "She's just too committed to this orthodoxy to accept that Americans don't want jihadists brought here by their own government."

Obama is scheduled to address the United Nations Tuesday with broad remarks about the state of U.S. foreign policy, which will undoubtedly include a call for more admissions of Syrian refugees into the U.S. and other countries around the world.

In the afternoon, he will host the Leaders Summit on Refugees and underscore the gravity of the refugee crisis in which more than 65 million have been displaced worldwide, the largest number since World War II, according to the White House.

From Syria alone, nearly 5 million refugees have left the war-torn country, Samantha Power, the U.S. ambassador to the United Nations, told reporters late last week in previewing the summit.

"All of these individuals, every one of these numbers is a face and a person with a family," she said. "They are facing very uncertain futures and they're looking to the rest of the world and to the U.N., of course, for help."

Power said several countries, including the U.S., are going to be pledging more slots for the resettlement of refugees. "You're going to see a range of announcements by different world leaders," she said.

The U.S. under Obama's direction has admitted 10,000 Syrian refugees already this year, and will increase those commitments in the final months of his administration with the goal of accepting 110,000 Syrian refugees by next October. But that figure will depend on the next president's views and policies.

Power also argued that the U.S. can admit the refugees while "ensuring our own security."

"As a country that's admitted 3.2 million refugees since the 1970s, we are more than capable of doing that and ensuring our own security, and the highest levels of security checks are in place for the refugee program," she told reporters.