President Barack Obama is playing a perilous political game with some of his core constituencies, pursuing policies that threaten to diminish the enthusiasm of groups that helped put him into office.

[IMGCAP(1)]In his first nine months, Obama has followed an agenda that raised concerns among unions, Jews, gays and Latinos — groups that backed him overwhelmingly and without which he cannot be re-elected. The complaints for now are mostly muted, and any damage done can be reversed. But all have high expectations for the president, and a few — particularly labor leaders and gays — view his presidency as the first, and perhaps the last chance for some time, to achieve long-coveted goals.

The president’s path among Jews is particularly tricky. Some 78 percent of Jewish voters backed Obama over McCain. They make up sizable voting blocs in swing states like Florida and Ohio, which Obama needs in his column. The president’s approval rating among Jews was at 64 percent in a recent Gallup poll — though the decline tracks that of other groups. An August poll of Israeli Jews, done for the Jerusalem Post, found that only 4 percent believe Obama’s policies are pro-Israel.

Statements by Obama and other leading administration figures in the early months of his presidency impressed many Jewish leaders as amounting to heavy-handed pressure against Israel. Obama appeared to be leaning on Israel to rein in its settlements on land captured from the Arabs while asking little of the Palestinians. At a June 4 speech in Cairo, Obama offered too much equivalency between the Jewish and Palestinian causes for some Jews.

A top U.S. Jewish leader noted that in recent weeks, Obama has smartly taken his effort to mediate Jewish-Palestinian relations behind closed doors, reducing the perception that he is hectoring Israel. He noted that, in the wake of the intifada, Jewish faith in the peace process has diminished, and Obama is not as free as President Bill Clinton was in the 1990s to try to pressure Israel to move the process along.

“If there are political consequences, they will come from the extent to which Obama tries to push Israel to do something that’s not in her interests,— the Jewish leader said.

Jews may also look toward the GOP in 2012 if Obama is not seen as acting forcefully to prevent Iran from obtaining nuclear weapons. The annual Survey of American Jewish Opinion by the American Jewish Committee last month found that 66 percent would support an attack by Israel on Iran. But for now, according to United Jewish Communities Vice President for Public Policy William Daroff, Obama’s approach of having negotiations with the threat of tough sanctions sits well with most Jews.

Obama has promised much to the gay community, and the pressure for him to deliver — as well as the growing frustration that he has not — is palpable. His agenda includes an end to the military’s “don’t ask, don’t tell— policy, legislation to bar discrimination against gays in the workplace and a repeal of the Defense of Marriage Act, which limits how federal and local governments can recognize domestic partnerships and allow benefits. Obama may soon sign legislation that would make assaults on gays hate crimes.

Much of this was laid out in an Oct. 10 speech to the Human Rights Campaign in Washington, D.C. The remarks were well- received within the hall but not universally applauded outside of it.

The speech was picketed by dozens of gay activists. Critics have focused on the lack of a timeline for fulfilling many of his promises. “The expectations were very high,— wrote Joe Sudbay, a prominent gay blogger. “The president spoke for approximately 25 minutes. And, tonight, he did not deliver anything new or exciting. He did not assuage our concerns.—

Labor officials, for their part, wait for an aggressive campaign by Obama to pass the Employee Free Choice Act — or “card check— legislation — something they expected the president to get forcefully behind.

The health care bill presents several minefields for Obama’s relations with the unions.

A Senate Finance Committee bill provision — which Obama has backed in principle — taxing “Cadillac— health care plans is vigorously opposed by union officials because it could hit many union workers who have negotiated healthy insurance benefits. And unions back a public insurance option to compete with private insurers. Obama does, too, but has suggested he won’t require it.

Labor leaders will also be watching closely if Obama gets serious about passing immigration reform. They’ll want to be sure that he is careful not to institute a robust guest-worker program.

Failure to make a sincere stab at immigration reform would hurt him with Hispanic voters, according to Brett Wilkes, executive director of the League of United Latin American Citizens. About two-thirds of Hispanic voters cast their ballots for Obama in 2008.

But Obama has some room to maneuver among Latinos since, Wilkes notes, immigration is not on the top of their list of priorities.

Instead, like everyone else, they are deeply concerned about the economy, health care and education. A good performance by Obama on these issues could go a long way to mitigate damage that he might incur if immigration reform fails.