President Reagan today risked both a budgetary crisis in the federal government and a bruising confrontation with Congress by vetoing a $14.1 billion supplemental appropriations bill he described as "wasteful and unnecessary spending."

Unless Congress, which will return to Washington on Sept. 8 from its Labor Day recess, either overrides his veto or quickly agrees on a new bill acceptable to Reagan, the president's action will jeopardize the nation's military payroll and the functioning of numerous agencies until the current 1982 fiscal year ends Sept. 30.

The 2 million men and women in the armed services will be paid on Aug. 31 only because Attorney General William French Smith has approved an unprecedented shuffling of government funds to make up for money included in the vetoed supplemental for military pay raises.

"Unless the Congress acts quickly upon its return to pass a [new] supplemental," White House spokesman Larry Speakes warned today, "our ability to meet the Sept. 15 military payroll will be in almost certain jeopardy."

But Reagan's ability to strike a deal with Congress on a new supplemental appropriations bill for the rest of the current fiscal year also has been jeopardized by today's veto, which was opposed by congressional leaders who closely cooperated with Reagan only little more than a week ago to push through a $98.3 billion tax bill the president regarded as important to economic recovery.

After the tax bill's passage there was talk of a new coalition reminiscent of the Eisenhower administration, with the president working with both Democratic and Republican congressional leaders to achieve an economic consensus.

Today, House Majority Leader James C. Wright Jr. (D-Tex.) said Reagan had touched off a "war with Congress" by vetoing the supplemental appropriations bill.

The hostile atmosphere is likely to be heightened by the confrontational wording of the veto message Reagan sent to the Democratic-controlled House, where the post-veto legislative fight will begin just two months before the fall congressional elections.

Observing that the supplemental appropriations bill contained $367 million in funding for social spending items he vetoed last June and $892 million in funding that was cut by Congress last fall, Reagan said: "This simply is not tolerable in the face of triple-digit deficits, and I cannot endorse these unwarranted spending increases."

Among other contentions he made in denouncing the supplemental, Reagan said, "This will bust the budget by a billion dollars."

In a nationwide radio address delivered from his ranch 29 miles northwest of Santa Barbara, the president used milder language. He stressed the idea that Americans are "pulling together" again as they did in World War II -- this time to achieve economic recovery.

While Reagan acknowledged that "we're not out of the woods yet," he was bullish on the prospects of recovery and contended that the veto kept his commitment to reduce deficits by cutting government spending.

Wright, responding for the Democratic Party, not to the words of the radio speech but to the action of the veto, said Reagan had reopened hostilities with Congress at the time it was being most cooperative.

The veto, Wright said, "revives the spirit of confrontation and hostility which some of us had tried to put at rest."

The confrontation is likely to occur after Congress reconvenes Sept. 8, the day after Reagan also is scheduled to return to Washington, because the mechanism used to meet the Aug. 31 military payroll, for which the vetoed supplemental contained $6.1 billion, is only a stopgap. Speakes described the expedient as "a one-time, temporary emergency regulatory change."

This change, which the attorney general ruled is legal under what Speakes termed "an extraordinary situation," allows the Department of Defense to defer until Sept. 30 paying the Treasury the income tax and Social Security deductions that it will withhold from the Aug. 31 military paychecks.

It is an unprecedented action that would be forbidden a private business unable to meet its payroll.

White House officials who recommended the veto to Reagan, both to hold down budget deficits and to please conservative Republicans unhappy with Reagan's $98.3 billion tax bill, said earlier in the week that the president would not reject the supplemental unless he could be assured the Aug. 31 military payroll would be met.

Because of the sensitive nature of the military payroll during an election campaign, the White House anticipates an immediate attempt to override Reagan's veto, the eighth of his presidency, after Congress returns. Only 67 members of the House voted against the supplemental, less than half of the 146 that would be needed to sustain the veto. Overriding a veto requires a two-thirds' majority of the House and the Senate.

White House counselor Edwin Meese III, one of the senior staff members who recommended the veto to Reagan, observed that the president had won several other congressional struggles in which he started out behind.

But Meese made no predictions about this one. "It's entirely possible we could lose," he said. "We know it's an uphill fight."

In his veto message the president complained that the bill provided far too much for domestic social spending and far too little for defense.

"While the enrolled bill includes $918 million in unrequested domestic increases, it provides only $0.5 billion of the $2.6 billion defense program supplementals I requested, a reduction of 82 percent," Reagan said, which prevents "required funding in virtually every major defense program . . . . "

The most likely casualty of the Reagan veto is one of his favorite projects: the $350 million Caribbean Basin Initiative.

Wright, a supporter of this economic assistance program for underdeveloped Caribbean nations, said he particularly regretted Reagan's "theatrical veto" because it would be difficult to persuade Congress to provide aid for Caribbean nations at a time when the president was cutting domestic programs for the poor and elderly.

Administration officials acknowledged that funding for the Caribbean program is in deep trouble, which was one of the principal reasons why Secretary of State George P. Shultz urged the president to sign the measure into law.

It may also be difficult to convince Congress to provide even the $500 million increase in defense spending contained in the supplemental, which Secretary of Defense Caspar W. Weinberger pointed out when he also unsuccessfuly urged approval of the bill.

In his veto message the president strongly appealed for preservation of the Caribbean initiative funding in a separate supplemental measure. "This funding is designed to resolve an unprecedented economic crisis that affects a strategic region located at our doorstep," he said.

"The Congress has also provided $50 million for special Lebanon emergency relief. This humanitarian assistance is essential for thousands of Lebanese civilians requiring aid."