AUGUSTA — The Appropriations Committee, halting and strained, finally reached unanimous agreement on a fiscal 1991 budget package late Tuesday night.

As the panel’s protracted deliberations concluded, the House and Senate gave all-but-final approval to one last, late-developing revenue-raising scheme — an additional $1 million assessment for state services to Maine’s unorganized territories.

The additional assessment, put at 13 percent above the current $7.7 million levy, was likened to a property tax increase and defended as an equitable, if unappealing way to spread the impact of a $210-million revenue shortfall throughout the state.

Appropriations Committee members also described it as an essential element in balancing the second year of the biennial budget.

Members absorbed by other duties and wearied by recent round-the-clock days of discussion moved slowly to resolve the last outstanding areas of disagreement.

“Almost everything has been resolved,” the panel’s Senate chairman, Democrat Michael D. Pearson of Enfield, told his colleagues as the Senate debated past 10 p.m. But more negotiations were needed, he added, and listed the unorganized territory assessment as “the main component” in matching spending levels with backup funding.

Shortly before 11:30 p.m., Pearson called for a show of hands on a motion by Rep. Linwood M. Higgins, R-Scarborough. The committee responded without dissent.

Despite the weekend infusion of $12 million in new revenue into the committee’s arithmetic, panel members were still scraping around for unencumbered funds Tuesday to cover a few small-ticket items.

The emerging budget package, designed to offset a projected revenue shortfall of $210 million through mid-1991, still relied on the 53 layoffs and related personnel savings built into Gov. John R. McKernan’s original proposal.

It also was dependent on a variety of revenue-generating initiatives, including Maine’s enrollment in the national Lotto America game and on a tax amnesty plan scheduled for later this year.

In one of the last compromises between majority Democrats and the Republican administration, both sides agreed to a $500,000 reduction in executive, judicial and legislative department payrolls, but left open the specific methods by which each branch would reach its target.

The budget panel’s slackened pace and desultory movement sparked a new round of speculation that legislative leaders, who have been shooting to adjourn the 1990 regular session a week ahead of the statutory deadline, might miss Thursday’s target and be forced to continue the session into next week.