By Roberta Rampton

WASHINGTON (Reuters) - Criticism of President Barack Obama's signature healthcare law by a top Senate Democrat this week laid bare post-election tensions that could pose challenges for the party in upcoming fights with Republicans over taxes, energy and immigration.

In a high-profile speech on Tuesday dissecting Democrats' losses in this month's midterm elections, Charles Schumer, the No. 3 Senate Democrat, listed "a cascade of issues" botched by the White House, starting with Obama's push for healthcare reforms soon after he took office in 2009.

Later on Tuesday, the White House took the unusual step of publicly pledging to veto a deal on tax breaks that Senate Democratic leader Harry Reid was trying to hammer out with Republicans in the House of Representatives.

"There is clearly a lot of unhappiness and a lot of mistrust that exists between the president and his congressional party," said Ross Baker, political scientist at Rutgers University.

Democrats will cede control of the Senate to Republicans in the New Year after heavy losses in the Nov. 4 elections that also gave the Republicans an increased majority in the House.

Obama, whose low approval ratings were seen as a drag on his party in the elections, may see support waver from some Democrats on an energy issue - the proposed Keystone XL pipeline to carry oil from Canada's oil sands to be processed on the U.S. Gulf Coast. Democrats in states where voters want pipeline will face a dilemma over whether to break ranks with Obama and back Republican legislation aimed at forcing the project through.

Republicans will also try to thwart the executive action on immigration that Obama announced last week and that grants temporary relief from deportation for millions of immigrants who are living in the United States without the right papers.

Several Democratic senators have been critical of Obama for taking executive action rather than letting Congress take the lead on the issue. If six or seven joined Republicans, they could block Obama's action, forcing a veto.

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'POST-DISASTER SYNDROME'

In some ways, Schumer's remarks were typical of the kind of "post-disaster syndrome" of finger-pointing common after election losses, Baker said.

"Typically, when a political party has suffered an electoral debacle, one of the first things they do is shoot the survivors," he said.

According to Schumer, the party lost because the White House messed up on "a cascade of issues," starting with the healthcare reform push in 2009, at a time when Americans were more preoccupied with the recession.

Also on Schumer's list of White House errors: the rollout of insurance marketplaces, fixing wait lists for veterans' hospitals, dealing with the first case of Ebola in the United States, and even security at the White House itself.

His remarks illustrated how some Democrats are trying to start to move apart and away from Obama.

"At this point now, Obama is not running for president again," said Matthew Green, associate professor of politics at the Catholic University of America. "But Democrats in the Senate are, and they want to get back the majority at some point. They are going to be thinking about, what can we say and do to help ourselves in next election cycle?" Green said.

Former Obama aides dismissed Schumer's comments as playing politics.

"Funny, I don't remember Chuck Schumer giving that advice when he was privately and publicly championing the Affordable Care Act in 2010," said Jon Favreau, a former White House speechwriter, on Twitter.

"So what exactly does Chuck Schumer believe was the error? Does he believe that the goal of winning office is winning office?" said Jon Lovett, another former Obama aide.

Top House Democrat Nancy Pelosi also rebuked Schumer, saying in a statement, "We come here to do a job, not keep a job."

(Additional reporting by Amanda Becker, Emily Stephenson; Editing by Frances Kerry)