The House yesterday opened debate on a Democrat-drafted budget for next year that has been denounced as "totally unacceptable" by President Reagan but described by House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) as likely to pass on a close vote.

O'Neill and other Democratic leaders acknowledged dissatisfaction among members over both defense and domestic spending levels in the nearly $1 trillion budget proposal and attempted to fend colleagues off with a variety of reassurances, including suggestions of more spending for defense after negotiations on a compromise with the Senate.

"This is just the early stage," O'Neill said in reference to the $285 billion allocation for defense in the Democrat-drafted plan, $35 billion less than Reagan proposed and $16 billion less than the Senate approved in its version of the budget last month.

Some key Democrats also have been concerned that the Senate and House Democratic plans underestimated actual outlays for defense in the budget, which could put a squeeze on funds for military readiness efforts. But a major revolt apparently was averted by assurances that the problem will be addressed in House-Senate negotiations over a final budget compromise.

Moreover, Reagan's case for a major increase in defense expenditures has been undercut by a budget alternative prepared by House Republicans, who are proposing $293 billion for defense, even less than the Senate allocated. The Republicans agreed yesterday to press for a vote today on their plan as a substitute for the Democratic draft, even while conceding it has little, if any, chance to pass.

There were also grumbles, especially among appropriations committee members, about proposed ceilings for domestic spending, which would be frozen or cut except for some "high-priority" social welfare programs.

Reflecting concern over complaints about individual program cutbacks, House Budget Committee Chairman William H. Gray III (D-Pa.) urged "those voices to look at the whole forest, not just the one tree that grows in their garden" and described the Democratic budget as "the best medium for an America that is getting terribly sick of red ink."

Republicans criticized the Democratic plan, approved by the budget committee on a largely partisan vote last week, on its handling of defense and taxes. Rep. G. William Whitehurst (R-Va.) complained that aircraft would be grounded, ship overhauls canceled and training and supplies cut under the plan. Rep. Delbert L. Latta (R-Ohio), ranking Republican on the Budget Committee, attacked the proposed tax increases of $7 billion more than Reagan wants, saying Americans want deficits reduced by cutting spending, not raising taxes.