The cast-of-hundreds conference between the House and Senate on President Reagan's spending cuts was kicked off yesterday with one of the principal players, Rep. Phil Gramm (D-Tex.), left grumbling in the wings.

Gramm became a hero to Reagan, and a renegade to Democratic leaders, when he helped line up conservative Democratic votes for the administration's budget targets and spending cuts, called Gramm-Latta in honor of Gramm and his cosponsor, Rep. Delbert L. Latta (R-Ohio).

There was little the Democrats could do about it at the time. But yesterday they retaliated by denying Gramm a place among the nearly 250 conferees, citing as a rationale his junior status on the Budget Committee.

Some Democrats susggested michievously that Gramm should be named as a conferee by the Republicans. But Latta, ranking minority member of the Budget Committee, said all the GOP slots were filled by Republicans.

"Del wouldn't appoint him," said Rep. James R. Jones (D-Okla.), grinning as reporters asked him why Gramm won't be a conferee. "I left it to Jim," responded Latta, also grinning.

Gramm claimed foul play, and the last word as well. "I intend to be standing there when the president signs it [the bill]," he told a reporter.

At a session attended by Budget Committee conferees from both chambers, Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) described the conference as the "largest ever" in both numbers and scope, although both he and his House counterpart, Jones, said they anticipate an agreement before the August recess.

There will be 72 conferees from the 100-member Senate and between 150 and 180 conferees from the 435-member House, involving nearly all their authorizing committees as well as the budget committees. They will probably never meet all together in one room, however, working instead in as many as 45 sub-conferences set up according to issues and committee jurisdictions.

The subject matter will be nearly $40 billion in mostly Reagan-proposed spending cuts approved by the two houses in somewhat different form last month. The House bill totals $37.3 billion, the Senate bill $38.1 billion, according to Domenici.

But, under painstakingly negotiated ground rules, the conference will be limited to points of substantive disagreement, covering about 20 specific issues. Domenici said. As specific issues, Domenici said. As much as 80 percent of the package can be resolved quickly and without difficulty, Jones said.

Domenici and Jones said the toughest issues were likely to include Medicaid, housing, health services block grants, telecommunications deregulation and Conrail funding.

The ground rules and "leadership understandings" are probably also as elaborate as those of any previous conference, aimed at preventing last-minute hitches and assuring approval before August.

Fearing such hitches, Reagan urged Senate Republicans to avoid a conference by approving the House bill. But they refused to do so, claiming to have received no-sabotage assurances from the Democrats.

As the Senate named its conferees, it instructed them to provide $950 million for the Head Start preschool program, which is what Reagan wanted. The House had deleted funds for Head Start, and the Senate provided $820 million.

Meanwhile, the House Appropriations Committee, approaching the half-way mark on its money bills, approved $13.2 billion for energy and water projects, including $228 million for the Clinch Riber breeder reactor and more money for nuclear weapons reseach, both of which Reagan wants.

A move to delete the reactor funding was defeated, 24, to 14. The bill also includes about $4 billion to continue water projects already under way.