President Barack Obama’s hold on his party’s liberal Members continues to fray after a series of tacks to the right by the White House — but they aren’t ready yet to abandon ship.

House liberals have been upset with Obama over his agenda for months, as they have felt taken for granted and ignored on a series of issues.

Congressional Progressive Caucus leaders chafed at his embrace of a tax on high-cost health insurance plans, his failure to fight for a public insurance option in the reform package and his troop buildup in Afghanistan.

And once health care reform is completed, Obama could soon face an uphill fight to get his fiscal 2011 budget plan approved, given wariness from his left flank at his expected attempts to cut spending and the deficit.

But despite tough talk from liberal House leaders, the bloc has rarely been willing to take on Obama with their votes. Many liberals vowed they would vote against any health care bill that didn’t have a robust public option, but that threat has appeared to be just that — a threat.

Progressive Caucus Co-Chairman Raúl Grijalva (D-Ariz.) said Wednesday that his group needs to “push the administration when it needs to be pushed, particularly right now on the health care debate.—

Grijalva said the administration needs to understand the political risks of dividing the Democratic Party’s base that a “Cadillac— tax on high-cost health plans poses, as well as concerns that liberals will stay home this year after the party set sky-high expectations and underdelivered.

Grijalva also warned that Progressive Caucus members are prepared to fight the president if his budget cuts their priorities in order to shrink the deficit.

“Where those cuts hit and who they affect is the base of our membership, and not only the Progressive Caucus but the Democratic Caucus,— Grijalva said. “We have to make sure that’s not balanced on the backs of the poor, on the backs of education and on the backs of people.—

The Arizona Democrat said that on the budget and other issues to come, including the looming need to reauthorize the No Child Left Behind Act and another jobs package, liberals want to have their ideas heard at the front end and not simply get caught reacting to proposals from the administration. But he said the goal is to get the administration in sync with Democratic base, not to create strife.

“We’re not picking a fight just for the sake of attention,— he said. “Our responses have to be strategic.—

That said, “I think the more comfortable we get in playing the role of good supporters, but also as able to question our allies, the better off we’ll be.—

The White House may be starting to listen. With new polls showing Obama’s popularity slipping, some have questioned whether liberals will simply stay home during the midterm elections this fall. But White House Press Secretary Robert Gibbs predicted Wednesday that voters will come around by November: “There’s a lot at stake.—

Grijalva also said that the talk of a close race for the Massachusetts Senate seat formerly held by the late Sen. Edward Kennedy (D) is another warning sign that the party’s base is in a period of “malaise.— Democrats are increasingly worried about losing Kennedy’s seat in next Tuesday’s special election as the race tightens between Attorney General Martha Coakley (D) and state Sen. Scott Brown (R).

“If we further demoralize our base, it’s not going to be a question of them voting for Republicans, it’s going to be a question of them not voting,— he said.

Rep. Peter DeFazio (D-Ore.), who has been outspoken in his criticism of the administration on a host of issues from transportation funding to dealing with the banks, said that a broader group of Democrats is now showing frustration given that Obama has embraced a tax on costly health insurance plans.

“A majority of the Caucus is not going to go quietly with the Obama agenda when we see it clashing with our basic values,— DeFazio said. “I think early on people gave him the benefit of the doubt,— DeFazio added, but are no longer doing so.

Progressive Caucus Co-Chairwoman Lynn Woolsey (D-Calif.) said the disenchantment with Obama has been bubbling up from constituents. “Now they are starting to be disappointed in us for not being able to get him to do what they want him to do,— she said, pointing to Obama’s failure to fight hard for a public insurance option and his embrace of the “Cadillac— insurance tax, in particular.

“The disappointment is progressives wanted to believe our new president is a progressive. He’s not.—

But while some on the left are talking tough, others are pointing to Obama as a vast improvement over President George W. Bush and note that Obama’s facing the difficult math in the Senate, where Democrats have a fragile 60-vote majority.

“On health care they are doing the best they can given the United States Senate,— Rep. Jim McGovern (D-Mass.) said. “You need 60 votes to have lunch in the Senate. That’s life. We’re going to have to deal with it. We need to get the best deal we can get, and that means the best deal we can pass. Otherwise this is all therapy.—

McGovern’s beef with Obama comes largely from his decision to send more troops to Afghanistan, a move that comes with a reported $33 billion price tag.

“Jesus Christ, that is a lot of money,— McGovern said. “That could do a lot of good here in the U.S.—

McGovern said that liberals like the president but also can debate him and prod him when they disagree.

“I love Obama, I’m glad he’s president. That doesn’t mean if I disagree I have to shut up,— he said. “We should engage in a full-fledged debate.—