By Sarah Chaney, Natalie Andrews, Wall Street Journal–

President Trump’s plan to bypass Congress to extend coronavirus economic relief came under fire from Democrats as insufficient and unconstitutional, while Treasury Secretary Steven Mnuchin defended the move and suggested any attempt to block it could backfire politically.

Mr. Trump’s plan, made public on Saturday after lawmakers and the White House failed to reach a deal on another aid package, calls for among other things funding $300 a week in special unemployment benefits, with an additional $100 coming from states.

Democrats had wanted to extend the $600 weekly additional benefits that were first approved in March and that expired last month, and House Speaker Nancy Pelosi (D., Calif.) and others said the plan not only didn’t go far enough but had breached congressional spending authority.

“Children are food insecure, families are at the risk of being evicted, the virus is moving like a freight train, even though the president has ignored and delayed and distorted what that is,” Mrs. Pelosi said on “Fox News Sunday.”

With the November election looming, however, any move to block the payments could backfire, Mr. Mnuchin suggested on the same program, adding that the White House was within its rights to move unilaterally.

“We’ve cleared with the Office of Legal Counsel all of these actions,” Mr. Mnuchin said. “If the Democrats want to challenge us in court and hold up unemployment benefits to those hardworking Americans that are out of a job because of Covid, they’re going to have a lot of explaining to do.”

Mr. Trump, a Republican, also issued on Saturday orders on payroll taxes, evictions and student-loan payments, issues that were all part of discussions on a broader aid package.

A possible legal challenge was just one question surrounding the orders.

Another was whether the states, strapped for cash because of the pandemic, would contribute the additional $100 in weekly benefits.

Democrats had wanted some $915 billion in state and local aid in their $3.5 trillion aid bill passed by the House in May. Republicans had offered $150 billion during negotiations.

Most economists had widely credited the $600 in additional weekly jobless aid as helping to keep the economy afloat while millions of people are kept home because of the pandemic, and some economists said the new relief measures were unlikely to provide a significant boost to the economy.

“The immediate economic benefit of this package is certainly higher than doing nothing, but it’s certainly lower than what a number of bipartisan congressional packages would be,” said Maya MacGuineas, president of the Committee for a Responsible Federal Budget, an independent bipartisan nonprofit.

“The relief is small, temporary, complex and unlikely to be effective in terms of the broader recovery,” said Donald Schneider, an economist at research firm Cornerstone Macro who formerly served as a GOP House aide. “I think it will be helpful in the sense that it’s likely to push the negotiators back to the table.”

Mrs. Pelosi called the actions unconstitutional, a view supported by Sen. Ben Sasse, Republican of Nebraska, on grounds that they usurp congressional spending authority.

Mrs. Pelosi also contended the measures are too meager for the continuing fallout from the pandemic. Democrats wanted to extend the $600 in special weekly unemployment benefits that expired last month, saying many people don’t have jobs to return to because their former employers have been forced out of business by the pandemic.

Executive orders tend to be especially contentious when they act as a substitute for legislation, which Mr. Trump’s order does, said Jonathan Turley, a law professor at George Washington University.

Mr. Trump also relied on a law that created funding for natural disasters like hurricanes as support for his plans to fund the expanded unemployment benefits. That, too, could present legal challenges, Mr. Turley said.

“There’s going to have to be some pretty creative arguments to suggest that Covid is some type of biological hurricane,” he said.

Legal experts said states must agree to provide the extra $100 in benefits, a big question given the hit to their finances.

“We’re looking at it right now to see whether we can do this,” Ohio Gov. Mike DeWine, a Republican, said on CNN Sunday. A former member of Congress, Mr. DeWine encouraged lawmakers to get back to negotiate a deal that would supply more federal funds to unemployment insurance.

The federal government would pay its share of jobless benefits through Dec. 6 by drawing on the Disaster Relief Fund, a source of money to pay for emergency costs. Mr. Trump set aside $44 billion from the fund, which has a balance of about $70 billion.

Mr. Trump’s order calls for states to draw on funds the federal government had distributed earlier in the crisis to pay their share of the jobless aid. More than $80 billion remains available for states to use through this funding source. States could also use their own sources of money to finance the additional $100 in benefits.

In other actions Saturday, Mr. Trump directed the Treasury Department to defer the 6.2% Social Security tax on wages for employees making less than about $100,000 a year. That suspension would last from Sept. 1 through Dec. 31. It is an unusual move, but it is within the administration’s authority during presidentially declared disasters.

If employers stop withholding those taxes, it would give workers a short-term increase in take-home pay but also create a looming liability in 2021 because the taxes would still be due eventually.

Mr. Trump said Saturday that he would ask Congress to waive any deferred tax liability and that he would try to make the payroll-tax cut permanent.

Democrats warned that such a move would defund and destabilize Social Security, with the party’s presidential candidate, former Vice President Joe Biden, calling the move a “first shot in a new, reckless war on Social Security.”

White House aide Larry Kudlow said on Sunday that what Mr. Trump meant was just the forgiveness for any deferred payroll taxes from this year, not a permanent change.

If all employers stopped withholding Social Security taxes it would put about $150 billion in workers’ pockets instead of government coffers, according to the Committee for a Responsible Federal Budget. But it is far from certain that employers will do so because of practical and legal concerns.

If Congress doesn’t ultimately approve the tax cut, employers that stop withholding now might have to withhold more later to make up the difference. And they could be on the hook for taxes that weren’t withheld from the paychecks of employees who later leave. The Treasury Department hasn’t yet issued formal rules on how the tax deferral would work and what employers should do.

Mr. Trump’s action applies only to the employee’s half of Social Security taxes. Earlier this year, Congress voted to let employers defer payments on their half of the Social Security tax until 2021 and 2022.

Mr. Trump also said that Americans with federally held student loans would be able to suspend monthly payments through Dec. 31, and that the government would waive interest on the loans during that period. Monthly payments have been suspended since the spring under the Cares Act, which had called for payments to resume after Sept. 30.

The president also signed an order directing his administration to take “all lawful measures to prevent residential evictions and foreclosures” related to the pandemic, though he didn’t extend an eviction moratorium for federal housing.

Write to Sarah Chaney at sarah.chaney@wsj.com and Natalie Andrews at Natalie.Andrews@wsj.com