Republican members of Congress said last night that they hoped President Reagan's invitation to House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) to "work together" on the problems of the federal budget would lead to an early bipartisan "summit" on the deficit issue that dominates the 1986 session.

Democrats expressed skepticism about Reagan's intent and said the blame for the deficits would come to rest on Republican shoulders in the November election.

On Capitol Hill, Reagan's State of the Union message drew praise from Republicans and a tip of the hat from Democrats. But the focus was on the signal some saw that the president is ready to deal on the deficit issue embodied in the new Gramm-Rudman-Hollings target of $144 billion for fiscal 1987.

Sen. John Heinz (Pa.), chairman of the Republican Senatorial Campaign Committee, said he thought it was "more than a formality" and expressed the hope that it presages "an invitation to a bipartisan budget summit. I don't see how else we can reach" the budget goal, he said.

The same wish was expressed by Senate Majority Leader Robert J. Dole (R-Kan.) and Budget Committee Chairman Pete V. Domenici (R-N.M.). Democratic reaction was mixed and skeptical, however.

House Democratic Whip Thomas S. Foley (Wash.) said, "We're willing to think it's an opening." But Majority Leader James C. Wright Jr. (D-Tex.) called the speech "more meringue than apple pie," and O'Neill termed it "a disappointment."

In their formal, televised response to Reagan's message, the opposition party spokesmen argued that the president's "failed fiscal policies" and massive trade deficits have "closed the door of opportunity" to farmers, small businessmen and young job-seekers.

The Republicans, as expected, praised the president's message, while carefully minimizing the disagreements many have expressed with the tax-revision plan and budget priorities at the center of Reagan's domestic program.

Dole, who is at the focus of those conflicting pressures, said Reagan "hit all the right notes" in his speech, but added, "Let's face it, the administration's agenda is jam-packed with thorny issues . . . . They've got their work cut out."

Only if "we in Congress and the administration join forces," he said, can the deficits be cut.

Sen. Gary Hart (D-Colo.) said Reagan's "problem is not with the Democrats but with the Republican leadership of his own party, who know full well that you can't balance the federal budget without revenues. The president is the last holdout, and he will have to work that out with his own party."

But despite their condemnation of the deficits, the Democrats made it plain they will not initiate any form of tax increase until Reagan "holster s the .44 magnum, 'make-my-day' veto gun," as House Budget Committee Chairman William H. Gray III (D-Pa.) put it.

Recently retired Virginia governor Charles S. Robb (D) said in a prespeech briefing that governors of both parties believe that new revenues have to be part of the budget solution. But Robb, too, said, "Until the president will bite that particular bullet, I don't think we are going to make any real progress."

The Republicans, particularly in the House, cheered Reagan's reiteration of his opposition to any effort to boost taxes.

In their televised response, the Democrats spotlighted their main political objective this year -- regaining control of the Senate. Sen. George J. Mitchell of Maine, chairman of the Democratic Senatorial Campaign Committee, served as master of ceremonies, and the Democratic contenders in two featured Senate races -- Lt. Gov. Harriett Woods of Missouri and Rep. Thomas A. Daschle of South Dakota -- were given national exposure.

The emphasis on new faces was consistent with Mitchell's insistence that this year marks the start of "the post-Reagan era." Having failed to dent the president's personal grip on voters, Democratic strategists said their best hope was to "move the debate beyond him."

Mitchell's closing comments blamed administration policies for "driving more families into hard times . . . and causing American jobs to move overseas." Trumpeting the trade issue, he said, "It will be a bitter irony if we lose the trade war after winning the World War. But we are losing it."

Mitchell also set out to capture the tax-reform issue for his party, noting that while Reagan has made it the centerpiece of his second-term domestic program, "Democrats first proposed tax reform. Democrats in the House passed tax reform."

Rep. Guy Vander Jagt (R-Mich.) praised the "balance of compassion and practicality" in Reagan's upbeat message and said Congress can meet the budget deficit target for this year, without a tax increase, if Democrats just "stop the 'gloom-and-doom' drumbeat."

Reagan's plea that defense spending be spared from cutbacks drew support from one Republican member of the Budget and Armed Services committees. Sen. Dan Quayle of Indiana, one of the 22 Republicans in seats up for election, said, "The buildup must be maintained for there to be progress in our arms-reduction talks with the Soviet Union."

Democrats left the issue to Robb, who said that "America has to be strong enough to defend our basic values and our freedom. But money alone won't make us strong. It's time to focus on what we get for our money . . . . "

In blunt language, Robb declared, "If defense spending has to be reduced, then let's reduce it. If domestic spending has to be cut, then let's cut it. If tax breaks have to be stopped, then let's stop them. It's going to take all of these steps, and all of us know it."