Three days after President Reagan told Americans to "count heads and take names" of those in the House who helped defeat a constitutional amendment to balance the budget, Rep. James R. Jones (D-Okla.) was back home in Tulsa cutting television commercials to explain his vote against the president.

His Republican challenger, Tulsa businessman Richard Freeman, was on his way to Washington looking for credibility, armed with new poll data suggesting that Jones, chairman of the House Budget Committee, has been hurt by his confrontations with the president and by a $100,000 negative ad campaign by the National Conservative Political Action Committee (NCPAC).

Freeman, who lost to Jones in 1980, is hoping to persuade national Republicans and political action committees that Jones is a worthwhile target in the final weeks of the 1982 campaign. Campaign officials say they are ready to listen, but are making no promises.

"The numbers look very encouraging," said Rick Shelby, an Oklahoman who heads the Republican National Committee's Target 82 program this fall. "We're waiting to take a closer look to determine just what Jones' vulnerabilities are. If the numbers reflect on close scrutiny what they show at face value, he is vulnerable."

For weeks, telegrams from Tulsa have been arriving at Republican headquarters in Washington with the message that Jones could be beaten.

Up to now, Republican officials have been inclined to ignore them. A 10-year veteran of the House, Jones has been identified as a rising star in Washington, hardly the kind of target the New Right or the Republicans have enjoyed knocking off in the past.

He is a fiscal conservative, a defender of the oil industry and a friend of business. When NCPAC tried to run television commercials attacking him as a liberal big spender, local stations in Tulsa refused to carry them.

But a new poll by Houston poll taker V. Lance Tarrance has reopened the case. Freeman said the poll shows him trailing Jones by only 10 points in a head-to-head contest. More important, he said, the poll indicates that there is resentment toward Jones for opposing Reagan and playing national politics at the expense of his district.

"He's lost his Boy Scout image," one Republican said.

Republican Party officials said this week that before they become more actively involved on Freeman's behalf they want him to demonstrate his ability to raise more PAC money.

By nearly every measure, Jones looks like a secure congressman. A White House chief of staff for Lyndon B. Johnson, he was first elected to the House in 1972, and quickly earned a reputation for fiscal conservatism and legislative acumen. With the recession still dragging on, his criticism of Reagan's budgets looks more prophetic.

But he represents one of the most Republican districts in America held by the Democratic Party, and he has had a difficult two years as the Democratic point man on the budget, made even more difficult by NCPAC.

Despite the rebuff by local television stations, NCPAC carried on an ad campaign attacking Jones in newspapers.

The NCPAC-sponsored committee to defeat Jones recently packed up and left, but the attack has been picked up by Freeman in his television advertising.

Freeman's messages are a textbook example of a negative campaign strategy. He has critized Jones for opposing Reagan, for voting for a back-door pay raise for members of Congress and for opposing the balanced-budget amendment.

Last week's vote on the budget amendment is indicative of the kind of tightrope Jones has been walking. Two months ago, at the national governors conference in Oklahoma, he delivered a blistering attack on the amendment. Last week in the House he supported the Democratic alternative.

Now he is telling constituents in his ads that he opposed the Republican version because it "would have vastly expanded the powers of the federal courts and the presidency."

He is also selling pork and prestige. "We've done a good job of explaining to people that the power and stroke he has as Budget Committee chairman have helped him represent them better," said Aloah Kincaid, Jones' campaign manager.

Jones remains apparently confident in the face of the Republican's attacks. He beat Freeman by 58 to 42 percent two years ago and says he will do that well again this year.