House Democratic leaders gave the go-ahead yesterday for preparation of a fiscal 1987 budget that anticipates inclusion of tax increases proposed by the Republican-controlled Senate, although they reserved the right to drop the tax proposal if it fails to win bipartisan support.

The House Budget Committee, whose Democratic majority has prepared a plan that includes the tax increases, will begin its formal markup of the budget today, hoping for signs of Republican support before it finishes, possibly not until next week.

Leadership sources indicated that the tax-increase provisions will be dropped from the budget if Republicans have not indicated support before the final vote on the plan.

Still leery of being attacked by President Reagan for advocating tax increases, Democratic leaders gave conditional assent to inclusion of the Senate's tax proposal to reduce next year's deficit below the $144 billion required by the Gramm-Rudman-Hollings budget-control law.

This means the Democrats could still meet the $144 billion target even if they drop the tax increases, which amount to about $7 billion more than the $6 billion in revenue increases that Reagan wants for next year.

It would also enable them to claim that they are suggesting taxes only to reduce deficits below the $144 billion level that both Reagan and the GOP-controlled Senate proposed -- or to increase defense spending, if that is the price of Republican support for a tax increase.

And, if those ideas fall flat, Democrats could remove their fingerprints from the tax increase before the ink is dry.

"What this comes down to is not tax-and-spend. It's tax-and-save," said one of the Democratic strategists, alluding to Reagan's disparaging references to Democratic "tax-and-spend" policies.

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) has been insisting on support from Reagan or such House Republicans as Minority Leader Robert H. Michel (R-Ill.) before he will ask Democrats to support a tax increase.

Reagan criticized the tax proposal when the Senate approved it last week. And House Minority Whip Trent Lott (R-Miss.) said House Republicans are "not inclined" to support tax increases beyond what Reagan advocates. But Lott said he would not "close the door" on taxes, especially if the Democrats were willing to compromise on spending policies. "If it's a blend that looks pretty good . . . we'd have to look at it," he added.

Democrats on the House Budget Committee have proposed less for defense and more for domestic programs than the Senate approved. They agreed yesterday to raise their proposal of $282 billion in defense spending authority for next year to $285 billion, contingent upon Pentagon accounting of spending windfalls resulting from declining inflation. The figure would still be slightly lower than this year's defense total of $287 billion. The Senate approved $301 billion for defense. Reagan requested $320 billion.

Responding to O'Neill's bid for bipartisan cooperation, Michel said Republicans are "ready to contribute" but added, "If it's all going to be doled out to us on a take-it-or-leave-it basis, then you can't have a bipartisan approach." As for taxes, he asked, "How can I make a commitment to something I've not even seen?"

House Budget Committee Chairman William H. Gray III (D-Pa.) held a preliminary discussion yesterday with Rep. Delbert L. Latta (R-Ohio), ranking Republican on the budget panel, but no agreements were reached.