President Obama, for all the flak he took from Republicans over his combative State of the Union address, now is running into turbulence from members of his own party – who could prove an even bigger barrier to his agenda.

Democrats from across the political spectrum spent Wednesday taking aim at parts of the president’s platform. Though in the minority, they hold sway because Democratic defectors – particularly in the Senate – could make the difference in helping Republicans pass key legislation, and even override a presidential veto.

Already, a top-ranking Senate Democrat has renewed pressure on Obama to slow his diplomatic outreach to Cuba and to Iran. House and Senate Democrats also convened a press conference on Wednesday to blast his push for new free-trade deals. Meanwhile, Democrats are likely to play a big role in advancing a bill in the Senate approving the Keystone XL pipeline.

On Wednesday, Sen. Bob Menendez, D-N.J., leveled some of the toughest Democratic criticism to date regarding the president’s foreign policy.

On the day the U.S. opened historic talks with the Cuban government in Havana, Menendez, who is Cuban-American and is the top Democrat on the Senate Foreign Relations Committee, sent a letter to Secretary of State John Kerry warning about the Castro regime’s intentions.

“Mr. Secretary, after five decades of authoritarian, one-party rule, we must recognize that the Castros will never relax their iron-fisted control over Cuba unless compelled to do so,” he wrote. “As the Administration pursues further engagement with Cuba, I urge you to link the pace of changes in U.S. policy to reciprocal action from the Castro regime.”

Menendez voiced concern that a few of the political prisoners released by Cuba as part of the deal were rearrested, and about U.S. fugitives hiding out in Cuba, among other issues. He said all these matters must be addressed before re-establishing diplomatic ties.

Shortly afterward, the senator scorched administration officials at a Senate committee hearing over their pushback on lawmakers’ effort to set up new potential sanctions against Iran. The legislation would provide for sanctions if Iran does not strike a deal with the U.S. and other nations curbing its nuclear enrichment program.

Obama, in his State of the Union address, said this legislation would "all but guarantee that diplomacy fails,” and threatened to veto.

Antony Blinken, deputy secretary of state, also said at the Senate hearing that “new sanctions at this time are both unnecessary and, far from enhancing the prospects of negotiations, risk fatally undermining our diplomacy.”

But Menendez scolded the administration witnesses. “Iran is clearly taking steps that can only be interpreted as provocative,” he said. “Yet the administration appears willing to excuse away any connection between these developments and signs of Iran's bad faith in negotiations.”

He also said the more he hears from the administration, “the more it sounds like talking points that come straight out of Tehran. And it feeds to the Iranian narrative of victimization.”

Not only could Menendez and his fellow Democrats help pass the Iran sanctions legislation out of Congress, but they potentially could provide Republicans enough votes to override the threatened presidential veto.

On another front, liberal House and Senate Democrats on Wednesday spoke out against Obama’s call for authority to fast-track pending trade deals with Europe and Asia.

In the State of the Union speech, the president said he wants the authority to “protect American workers, with strong new trade deals from Asia to Europe that aren’t just free, but are also fair.”

“It’s the right thing to do,” Obama said. “I’m the first one to admit that past trade deals haven’t always lived up to the hype, and that’s why we’ve gone after countries that break the rules at our expense. But 95 percent of the world’s customers live outside our borders. We can’t close ourselves off from those opportunities.”

But many Democrats, and union leaders, say these kinds of deals cost U.S. jobs, and point to the Clinton-era NAFTA deal.

Rep. Louise Slaughter, D-N.Y., on Wednesday vowed to fight the proposal “tooth and nail.” She and other Democrats argued the push would hurt American workers.