House Democratic leaders called President Reagan's bluff yesterday in a high-stakes election campaign gambit and decided to bring to the House floor today a balanced-budget constitutional amendment.

The sudden switch in strategy amounted to a preemptive strike to keep Reagan from blaming House Democrats for bottling up the amendment, which has already been passed by two-thirds of the Republican-controlled Senate.

The Democrats' move was disclosed just hours before Reagan made his second visit to Capitol Hill this year to push personally for the amendment's passage.

It came a day after Republicans, led by Vice President Bush, struck first by rounding up enough petition signatures to force the amendment to the House floor for a vote later this month, if Congress remained or was called back into session.

The outcome of today's vote could help shape the major economic issue of the Nov. 2 congressional election. Reagan is seeking to focus voter attention on the balanced-budget amendment, while Democrats want to emphasize what they call "Reagan's recession."

When Reagan appeared yesterday at a Capitol Hill reception honoring the 218 House members who petitioned to bring the balanced-budget amendment to a vote, he warned against what he called "11th-hour sleight-of-hand" tricks to foil the measure's passage.

Democrats countercharged that Reagan was pushing the amendment as a diversionary tactic to keep voters' minds off the persistent recession and high unemployment. House Majority Leader James C. Wright Jr. (D-Tex.) called it "a rabbit run across the trail of the fox to distract the dogs."

House Republicans conceded they were caught off guard by the latest Democratic move without time to nail down the two-thirds majority necessary to pass a constitutional amendment. But Democrats were far from confident they could defeat it on a straight up-or-down vote.

So they scrambled into the evening to come up with an alternative to the Reagan-backed constitutional amendment, which would permit deficits only in times of war or when sanctioned by a three-fifths majority of both houses.

What they came up with was a substantially less restrictive amendment, under which the president would have to submit a balanced budget and Congress would have to follow suit unless it makes a "declaration of national emergency," in which case deficits would be permissible. No three-fifths "super majority" would be required to permit deficits. Moreover, the president would not be given new powers to enforce a balanced budget, as Democrats contend he would under the Reagan-backed proposal.

The Democrats' proposed amendment is similar in some respects to legislation proposed earlier by House Budget Committee Chairman James R. Jones (D-Okla.) but was rewritten and put in amendment form as a stronger antidote to the Republicans' plan.

Once the Democrats have their plan in hand, the leadership-controlled House Rules Committee cleared the way for back-to-back votes today on both amendments--the Democrats' measure first and then the Republicans' proposal as a substitute, with simple majorities required in each case. However, whichever plan survives would then be subject to a two-thirds vote for passage as a constitutional amendment.

Reagan, appearing before Democratic as well as Republican supporters of the amendment in a House office building caucus room, described the measure as the most important step Congress could take to put the country on the path of a sustained economic recovery.

"We need and deserve a vote on this fundamental reform," he said, adding: "The time to act is now."

Some Republicans indicated, however, that now might not be the best time, at least tactically.

Under the discharge petition by which Republicans and their conservative Democratic allies sought to pluck the amendment out of a hostile House Judiciary Committee, the vote would have occurred, under rules governing discharge petitions, on Oct. 11, if Congress were in session that day. But the Democratic leadership will bypass that process by bringing the issue up itself, thereby controlling the timing.

"Clearly we wish it could have been later," after Republicans had time to round up more votes, said House Minority Whip Trent Lott (R-Miss.).

Rep. John H. Rousselot (R-Calif.), another key backer of the amendment, conceded that pro-amendment forces lacked the necessary 290 votes for passage at mid-afternoon yesterday.

Disclosing the Democratic decision to force a showdown on the amendment, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) accused Reagan of "wrecking the economy" and then trying to deflect attention by focusing on the fight over the amendment.

"I hope he brings a balanced budget with him" when he comes to Capitol Hill, said O'Neill sardonically, referring by implication to the fact that Reagan's own budget for the fiscal year starting today anticipates a deficit of more than $100 billion.

With Congress hoping to quit this weekend, O'Neill said that consideration of the amendment today would eliminate the possibility that Reagan might summon Congress back into session during the campaign to act on the issue. "Knowing the political nature of the man, I presume he would be calling us back," said O'Neill.

There had been rumors Reagan might do so. Although Republican lawmakers who checked with the White House said no such plans were under consideration, the rumors were encouraged in some GOP quarters to keep up pressure for action on Oct. 11.

The Senate passed a balanced-budget amendment by a vote of 69 to 31 earlier this year, but it differs from the version that has been discharged from the House Judiciary Committee in several ways, including language requiring a three-fifths vote of both houses to increase the national debt. The House measure does not contain that provision.

Under normal procedures, differences would be ironed out in a House-Senate conference. But because the conference could be thwarted by Democratic opponents of the measure, House Republicans said last night they would urge Senate GOP leaders to accept their plan if it is approved by the House. Senate approval of the House plan would obviate the need for a conference and complete congressional action on the amendment.

Senate Majority Leader Howard H. Baker Jr. (R-Tenn.), a supporter of the amendment, has said he would try to keep the Senate in session, at least informally if necessary, to await the outcome of the House vote.

While still scrambling to come up with an alternative, O'Neill described the Republicans' proposed amendment as "lethal" to the country in its implications for the economy.

Wright also contended that it would hand the president virtual "dictatorial powers" by requiring that he ensure spending does not exceed the limits of a balanced budget. Wright said the president could refuse to spend any money he didn't want to spend, whether for defense projects or Social Security benefits.

It's like "playing Russian roulette" with the Constitution and its balance of powers between the executive and legislative branch, said Wright.

He also compared Reagan to "Nero fiddling" as the president campaigns for a constitutional amendment for the future while the recession deepens now.