Among the countless responses last week to President Carter's State of the Union and budget messages was an offering from a pillar of conservative Republicanism, California's Rep. Barry Goldwater Jr., who crystallized his reaction in the headline he put at the top: "Jimmy Carter Jakes Me Feel Good."

Noting Carter's decision to increase defense spending, Goldwater said he had watched liberal congressional Democrats "squirming uncomfortably" as their party's leader set forth his relatively conservative budget plan for the year.

If Goldwater had looked harder, he might have noticed that the discomfort Carter has created is not limited to liberal Democrats.

The events of the past week, which might be considered Round One of the 1980 presidential campaign, have created a quandary for the Republican Party and for the GOP's long roster of presidential hopefuls. The Democrat in the White House has occupied their fortress, and the Republicans appear, temporarily at least, to lack a clear strategy for counterattack.

Three of the GOP presidential contenders -- John Connally, George Bush, and Ronald Reagan -- made it their business to be in Washington last week. But once they got here, all three seemed puzzled about how to respond to the conservative thrust of Carter's messages.

The GOP dilemma was evident, too, at the Sheraton Park Hotel, where the Republican National Committee held its midwinter meeting. Party chairman Bill Brock and the issue-oriented experts he had lined up to responed to Carter found themselves agreeing with the president nearly as often as they differed with him.

At a session designed to outline for state party leaders the GOP response to Carter's proposals for defense and domestic spending, Brock had to admit that "we Republicans can't quarrel with either of those priorities."

On domestic matters, the quarrels that Brock raised were matters not of kind but of degree. He said the president had not gone far enough in his pledge to cut spending and had not pledged to veto congressional initiatives that would conflict with the proposals in his budget.

Presenting the GOP response to Carter's defense proposals, Fred Ikle, who headed the Arms Control and Disarmament Agency in the Nixon and Ford administrations, had more direct criticisms of the president. He warned that the upcoming strategic arms limitation treaty (SALT) might lock the United States into a position of military inferiority, and said Carter had not responded adequately to recent "failures" of U.S. intelligence, such as not predicting the upheaval in Iran.

But like, too, had to agree that the basic direction of Carter's defense policy "was not something with which Republicans can sharply differ."

Connally, Bush and Reagan took different tacks in struggling to draw a clear line with Carter.

Reagan deliberately decided not to try. In three days on Capitol Hill, he avoided taking a public stand on a single issue or replying to Carter's budget message and State of the Union speech. And when pressed on specific issues in private meetings with senators and House members, the former California governor spoke only in general terms.

Bush and Connally, both Houston lawyers, found themselves agreeing with Carter on several crucial economic questions.

Bush, for example, conceded his own anti-inflation program "is not different from what Carter says he's doing." Connally put some distance between himself and the president by calling for a 5 percent cut in all federal spending and a constitutional amendment requiring a balanced federal budget. But later he found himself saying, "I applaud" Carter's decision to increase defense spending and describing Carter's wage-price guidelines as "the only reasonable approach" to combating inflation.

Republican presidential hopefuls did only slightly better on foreign policy. A spokesman for Reagan, for example, said the former governor felt it was too early to decide a position on SALT II. Bush took a similar position, while Connally said, "my inclination is to oppose" SALT II.

Both Texans adamantly criticized Carter for giving in to Chinese demands without getting anything in return in the negotiations to normalize relations with the mainland. But Bush, former chief of the U.S. liaison office in Peking, conceded he had long supported formal recognition of the People's Republic of China.

All in all, there was no real winner in the Round One jockeying. Although the Republican National Committee was in town for much of the week, there was no real groundswell of support for anyone.

Southern Republicans, both in Congress and at the RNC meeting, expressed far more sympathy for Connally -- who switched parties six years ago -- than did their northern counter-parts. "We were all originally Democrats in my part of the country. So we have a natural affinity for Connally," said Rep. Trent Lott (R-Miss.). "But I don't think the press is going to let him forget that trial of his." (Connally was acquitted four years ago of a charge that he took $10,000 in bribes to boost dairy price supports.)

Reagan's three days on Capitol Hill were perplexing ones. His great accomplishment was that he got so many people to sit down with him: 35 senators, including such key Republican liberals as Sen. Jacob Javits (R-N.Y.) and Sen. Charles McC. Mathias (R.-Md.) and almost two score House members.

What he gained was another matter. Reagan said he made it clear to everyone he talked to that "I didn't come to town with any pledge cards. And I'm not leaving with any."

However, he did open lines of communication with congressional Republicans, lines he intends to improve in months to come. "The better you know a guy the more difficult it's to come out against you," said Reagan strategist Johns Sears.

Most of the senators and House members Reagan met are a cautious lot, too pragmatic to throw their support behind anyone's candidacy 18 months before the party's nomination convention. "Most of us are keeping our powder dry at this point," Sen. H. John Heinz III (R-Pa.) said after meeting with Reagan.

But there were those, mostly conservatives, eager to jump on a Reagan bandwagon whenever it starts rolling. Lott, for example, said he supported President Ford in 1976 rather than Reagan "and I'd like to correct that." Roger Jepsen, a new Republican senator from Iowa, indicated he's leaning strongly toward Reagan and will be making a decision in not too many months.

Reagan, far better known and organized than any of his rivals, seemed more worried last week about making any mistakes that might return to haunt him than saying anything critical of the Democrats in the White House.

When given a golden opportunity to sound off against Carter the morning after Carter's State of the Union address, Reagan didn't even mention it during a speech at the Mayflower Hotel.

Reagan, said adviser Sears, had decided that replying to Carter was a job best left to Republicans in Congress. "To the extent that the Republican response is weak is testament to the blandness of everything Carter says," Sears said.