The nation's governors came here yesterday for a mid-winter meeting their leaders hope will thrust them into the center of the budget debate.

While a group of Democratic governors used a partisan news conference to call for scrapping of income-tax indexing and a cap on President Reagan's third-year tax cut, the bipartisan leadership of the National Governors Association sketched a plan aimed at cutting the projected budget deficit by two-thirds in the next five years.

As outlined by the current chairman, Utah Gov. Scott M. Matheson (D), and his successor, Illinois Gov. James R. Thompson (R), the governors' budget "guidelines" call for halving the pace of Reagan's defense buildup, freezing federal aid payments, cutting entitlement programs but fully funding programs that are based on proven need.

The guidelines also call for boosting revenues by at least $70 billion but do not spell out specific changes.

At the Democrats' news conference, Govs. John Y. Brown (Ky.), Michael S. Dukakis (Mass.) and James J. Blanchard (Mich.) advocated capping the 1983 tax cut at $700 per family and scrapping tax indexing, which is to begin in 1985.

They said it would save $127 billion over the next five years and bring down a deficit that they said threatens to cut short any meaningful economic recovery.

The governors' meeting, which begins formal sessions today at the Hyatt Regency Hotel, is expected to be dominated by debates on budget policy, jobs bills and energy.

Matheson and Thompson conceded that they are not sure how broadly the governors support getting into the debate on defense, entitlements and taxes. The guidelines will be discussed at a meeting of the executive committee today.

As outlined by Matheson and Thompson, the proposals would trim the deficit to $90 billion by fiscal 1988, almost exactly two-thirds less than now projected. Over the five years, there would be $286 billion savings in defense cuts or higher revenues, $177 billion on domestic programs and $69 billion in interest payments.

Smaller federal deficits would make it easier for states to balance their budgets, the governors said.