While most Americans squeezed an extra day off out of the one supposedly "working" day of the July 4th weekend, Sen. Arlen Specter (R-Pa.) spent yesterday working like the political equivalent of a one-armed paperhanger.

Over 14 hours, he appeared at five open-house town meetings in Pennsylvania in which he took questions from voters, sat in on a veterans' hospital hearing, met with the editorial board of the Scranton Times and wound up the day with a dinner speech in Lewisburg (population 5,400). His schedule for today is a little easier -- five events over 12 hours, topped off by the 100-mile drive from Hazleton back to Philadelphia.

This is how it goes for Specter, a freshman who occupies one of the 22 Republican Senate seats that will be contested next year.

He does not now appear to be one of the most vulnerable of the Republicans who are up in 1986, but he is running in one of the most unpredictable and mercurial swing-states in the union. Pennsylvania Democrats enjoy a registration edge of nearly 900,000, and national Democrats have targeted Specter's seat in their drive to regain control of the U.S. Senate next year.

But on this Independence Day weekend, Specter has reason to breathe a little easier than usual, according to Pennsylvania politicians. On June 27 he had to cast another of the Perils of Pauline votes that Republican senators from marginal states have faced this year -- on confirmation of William Bradford Reynolds as associate attorney general, the number-three post in the Justice Department.

Specter, after typically weighing the pros and cons carefully -- and publicly -- joined the eight Democrats on the Senate Judiciary Committee and Sen. Charles McC. Mathias Jr. (R-Md.) in a 10-to-8 vote against recommending Reynolds to the full Senate. It was a stunning rejection of the chief architect of the Reagan administration's civil rights policies, and a stinging political slap at President Reagan.

Specter justified his vote on the grounds that Reynolds had "placed himself above the law" by ignoring court rulings on affirmative action and school desegregation and seriously misled the committee in his testimony by implying that he had opposed discriminatory election laws in Georgia.

There were some hints of retribution by the administration but Pennsylvania political observers didn't seem to be inclined to take them seriously. At the administration's behest, some businessmen lobbied Specter before the vote, but they appeared to be deflected by his explanation.

"There's no conservative GOP opposition up here to give him any flak, and certainly his Democratic opponent, whoever it is, isn't going to," said one. Specter's Democratic challenger is expected to be either Rep. Bob Edgar (D-Pa.) or state Auditor General Don Bailey.

In his 20 years in elective politics, Specter has won a relatively large share of the minority vote in Philadelphia for a Republican -- 25 to 30 percent. The black vote in the city helped him defeat former Pittsburgh mayor Pete Flaherty, his Democratic Senate opponent in 1980.

Next year, however, the Democrats are hoping that black political leaders led by Mayor W. Wilson Goode can hold Philadelphia's black voters in line for their candidate by concentrating on the impact of Reagan's policies on blacks.

Rather than counting on minority support, Specter is more likely to place his trust in hard work and running scared -- running terrified, some say.

He measures his travels around the state in community visits rather than the number of days. He made 194 community visits last year and 99 in 1983. His goal is to visit each of the 67 counties in the Commonwealth at least once each Congress and ideally once a year.

Specter's frenetic effort appears to be paying dividends. The National Republican Senatorial Committee has taken him off its list of the 10 most vulnerable Republicans for next year and put him on its list of the 10 most likely to succeed.

According to a poll taken last January by Republican pollster Robert Teeter, Specter's job approval rating has risen 15 points to 70 percent, and the respondents were in favor of his reelection by 60 percent to 30 percent. About 50 percent can name him as their senator without a prompting list, about the same number that can name Sen. John Heinz (R), Pennsylvania's senior senator and the state's most popular politician.

Specter has a campaign fund of nearly $1 million that is in the bank drawing interest until he needs it, and he anticipates little trouble raising the $6 million to $8 million his supporters say he'll need for next year's race (compared to about $2 million in 1980).

In the past two months, he has had Vice President Bush as the feature attraction for a campaign fund-raiser in Pittsburgh, Sen. Barry Goldwater (R-Ariz.) in Hershey, former secretary of state Henry Kissinger in Philadelphia and Sen. Ted Stevens (R-Alaska) in Scranton.

This is the sort of schedule expected of a politician who has been described as cold, calculating, ruthless, ambitious, opportunistic and -- yes -- publicity hungry. It is also the schedule of a man who has learned the hard way and who has kept firmly in mind that those who expect the worst will not, alas, always be disappointed.

"I run scared, that's accurate to say, but run hard is probably a better word," he said. "I've never seen an election that can't be lost. There are a lot of pitfalls: an economic downturn that people blame on Republicans, the historic cycle in the sixth year of a two-term president in which members of his party have troubles and countless others."

Specter, 54, has every reason to run scared. Twenty years ago he was the GOP boy wonder of Philadelphia, having switched from the Democratic Party to be elected district attorney, at the time the first Republican elected city-wide in Philadelphia since the early 1950s.

He was reelected to a second four-year term in 1969, but he lost the mayor's race in 1971, was defeated for reelection as district attorney in a shocking upset in 1973, lost the senatorial nomination to Heinz in 1976 and the gubernatorial primary to Gov. Richard Thornburgh in 1978.

Talking about the Senate, however, Specter sounds more like the small-town Midwest boy he used to be (born in Wichita, Kan., he grew up in Russell, Kan., Senate Majority Leader Robert J. Dole's home town) than a cold, calculating, ruthless, etc., politician.

"I had a rocky road getting here and I'm going to do my damndest to stay here. This is a fascinating job, challenging, demanding, a great opportunity to serve," he said. "Every problem in the world comes to the U.S. government and every problem in the government comes to the U.S. Senate."

As a member of the Judiciary Committee and a former district attorney, he is proud of his career-criminal bill, which makes it a federal crime for anyone with two previous convictions for robbery or burglary to be carrying a gun. Specter has also cosponsored legislation to fight child pornography and to deal with the problem of missing children. As a member of the Appropriations Committee, however, he is best able to look after his number-one priority -- Pennsylvania's economic interests, from keeping and attracting industry and jobs to funding for highway and bridge repairs.

One possible pitfall that makes Specter's supporters nervous are the tough votes to which President Reagan subjects Republican senators, such as funding for the MX missile, the federal budget proposals, and the Reynolds confirmation. Specter's handling of some of these sensitive votes also makes them nervous.

He voted for the budget compromise between the president and Republican Senate leaders even though it included a reduction in Social Security cost-of-living increases and eliminated Amtrak subsidies -- which are a major issue in Pennsylvania -- as well as urban mass transit subsidies and urban development grants.

Before he voted on the budget, Specter promised to offer amendments to restore these funds, but his supporters feared that he might be left twisting slowly in the wind. A good share of those funds was soon restored, however.

"I vote for the president as often as I can whenever he's not in conflict with Pennsylvania's interests," he said. "I knew there were political problems with it, but I voted for the compromise because we really have to draw the line on the budget and the compromise would have reduced it by $52 billion.

"I also support a constitutional amendment requiring a balanced budget. But I couldn't accept reducing the COLAs Social Security cost-of-living adjustments or eliminating Amtrak. People here and my Senate colleagues understand that a Pennyslvania Republican can be relected only if he shows some independence and pursues a moderate course."

Specter also made his supporters jumpy with his decision on how to vote on MX funding. He seemed to be opposed, which prompted administration spokesmen to hint that when senators running for reelection next year wanted the president to help with fund-raising, he would give first priority to his "friends."

Specter took this as a veiled threat, angrily telling an administration lobbyist that such a course was "destructive" and "devastating." Just to clear the record, he said, he did not want Reagan to come in to raise funds for him no matter how he voted. In the end, however, he supported the president and voted for the missile, on the grounds that the MX is needed as a diplomatic bargaining chip in the arms control talks in Geneva.

"He probably could have handled the MX vote a little better," said William A. (Billy) Meehan, a longtime Philadelphia Republican leader. "He didn't have to call a press conference to announce it."

That was typical of Specter's career, however. As a brainy, intense, rumpled lawyer and former district attorney, he brings great intensity to his issues as well as his campaigning. He examines both sides of the major issues, exhaustively and often publicly, so that people are often confused as to where he stands.

As district attorney, he also displayed a great flair for publicity, and his critics contend that he pays more attention to this than to follow-up on the substance.

"The radio reporters love him because when they ask for a comment, he asks if they want a 15-second or 30-second bite," said one Pennsylvania political observer. "He's a master of the 30-second television bite. There are people in Berks County who will swear that he was once the county DA because of all his travels through there when he was the Philadelphia DA back in the late '60s."

Specter responds that he is only meeting the requirements of doing the job and being reelected as a Republican senator from a state in which the Democrats have such an advantage in numbers.

"As a U.S. senator, you have to establish yourself so that people get to know something about you," he said. "I have a good base in eastern Pennsylvania because the DA's job is very high-profile if you're active, as I was. But to get known in the western part of the state and up in the northern tier of counties you have to travel."

While there is currently no prospect of a primary challenge, he faces the near-certainty of a tough Democratic opponent. Edgar, a five-term "Watergate Baby" House veteran, is expected to conduct a primary battle with Bailey, a former House member and the Democrats' only statewide office-holder.

For 10 years the liberal Edgar has bewildered and infuriated his Republican opponents by being reelected to his Delaware County district, which Republicans have long considered almost sacred GOP territory. For years he has been preparing for a Senate race by traveling around the rest of the state.

Bailey, who is from the Pittsburgh area, is a decorated Vietnam war hero, which plays well in a state that has provided more than its share of servicemen and therefore has a disproportionate number of veterans.

All this evokes one response from Arlen Specter: Run harder.