Senate Majority Leader Robert J. Dole (R-Kan.) warned bluntly yesterday that Congress will "go it alone" in developing a fiscal 1987 budget unless the White House joins in pursuit of a budget compromise.

Many of Dole's Republican colleagues said that such a break with the administration could result in a bipartisan budget unsatisfactory to President Reagan, probably similar to a plan approved last month by a majority of both Republicans and Democrats on the Senate Budget Committee.

The White House has condemned the committee proposal, which included $18.7 billion in tax increases and cut Reagan's defense request by $25 billion, and ruled out negotiations on an alternative. Dole, faced with sharp divisions among GOP senators on key budget issues, has been pushing to draw the administration into talks that might produce a compromise.

His comments yesterday indicated that Dole may be running out of time if not patience as Congress appears certain to miss its April 15 deadline for passing the budget.

In addition to threatening a go-it-alone budget, Dole aligned himself with rebellious Senate Republicans who warned earlier that failure to reach a budget agreement could stall the president's tax-overhaul plan.

In an interview on ABC-TV's "Good Morning America," Dole said he had "a little hint" for the administration. "If they are really serious about tax reform, they better start talking to us about the budget process, because if we don't get the budget process moving it's going to slow down the president's efforts at tax reform," he said.

Later, in remarks on the Senate floor, Dole warned that continued delay on the budget invites automatic spending cuts under the Gramm-Rudman-Hollings deficit-reduction law, which he said would slash $50 billion in spending authority from Reagan's $320 billion request for defense.

He said he hoped to meet with administration officials within the next few days "to find out exactly what role the White House wants to play in the budget debate." While it could be a "constructive and important role," he said, "if they [White House officials] are not interested, then Congress will have to go it alone."

Dole did not spell out what would happen next. But other Republican senators said a Senate impasse with the White House could lead to negotiations with the Democratic-controlled House and Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.). "If the White House doesn't participate, then he [Dole] will have to go across the Capitol . . . and meet with the speaker," said Sen. Thad Cochran (R-Miss.). This would produce a budget "pretty close" to what the Senate committee proposed, said Sen. Charles E. Grassley (R-Iowa).

Dole appeared more interested than many of his colleagues in pushing for negotiations with the White House.

"The only way to get a budget is to go ahead and vote," said Budget Committee Chairman Pete V. Domenici (R-N.M.), who showed little enthusiasm for negotiations and plans daily floor speeches calling for prompt action on the budget. "Frankly, I'm not so sure it wouldn't be quite appropriate this time around for the White House and the president to do nothing and let us do our thing," he added.

Even some senators such as Cochran who oppose the Budget Committee plan were skeptical about the chances for a negotiated settlement. "I don't see how you do it," Cochran said. "There doesn't seem to be any interest, except for Senator Dole, in putting something together."

Several senators attributed White House reluctance to negotiate to faith that a strong economy, coupled with administration pressure for constraints on appropriations bills, will produce a deficit low enough to avoid the Gramm-Rudman-Hollings cuts.

But many senators appeared skeptical, and a Budget Committee source said a deficit of at least $168 billion is likely even under the most optimistic economic scenario. Automatic cuts would be triggered if the deficit is not within $10 billion of the $144 billion target for fiscal 1987.