The House Oversight Committee has dropped its push to subpoena President Obama's budget director and will instead accept testimony from another White House official at a Thursday hearing on a proposed administration rule requiring federal contractors to disclose political contributions.

The chief government investigator in Congress was initially planning to subpoena budget director Jack Lew to probe why the White House is considering demanding disclosures of political contributions.

Rep. Darrell Issa, chairman of the House Oversight and Government Reform Committee, wanted to compel Lew to testify at a hearing Thursday after Issa was stood up by the budget director in a letter sent on Monday.

After facing Issa's threat of a subpoena, the Office of Management and Budget offered Daniel Gordon, who is in charge of OMB procurement, to testify. The committee then backed off its subpoena threat, a source close to the committee told Fox News.

Issa said in a written statement that the White House "made the correct decision" in offering up somebody from the administration to attend the hearing.

"I look forward to Administrator Gordon's testimony," Issa said.

However, a senior administration official told Fox News that while Gordon will testify about procurement policy, he will not be allowed to discuss the proposed executive order dealing with disclosure of political donations -- since the proposal is only a draft order and not current policy.

That could lead to a testy hearing Thursday. The relationship between the California Republican and the White House is already tense. Before Gordon was tapped to testify, Lew sent Issa a letter last week explaining that he couldn't testify because "this hearing concerns a draft presidential executive order that is still moving through the standard review and feedback process."

Issa responded with his own letter asking Lew to reconsider.

"If the OMB continues to demonstrate an unwillingness to cooperate fully with the committee's oversight function, we will be required to consider the use of compulsory process," he wrote.

Obama drafted the proposal last month, which is reminiscent of a provision in a Democratic bill called the Disclose Act that died in the Congress last year.

That bill would have required corporations and unions to identify themselves in political ads they pay for -- a response to a 5-4 Supreme Court ruling that upheld the First Amendment rights of these groups to spend money on campaign ads.

The proposed order would require government contractors to disclose all donations to federal candidates, political parties, committees or interest groups spending money on campaigns once the total exceeds $5,000 in a given year.

The White House has said the proposed order would provide transparency to taxpayers about political spending by government contractors.

But Rep. Steny Hoyer, the No. 2 Democrat in the House, said he disagreed with the proposed draft.

"I'm not in agreement with the administration on that issue," Hoyer said. "The issue of contracting ought to be on the merits of the contractor's application and bid and capabilities."

He and Republican lawmakers are concerned that a disclosure requirement could introduce politics into the contracting process. Some theorize that some contractors could be "blacklisted" if they haven't made the appropriate contributions to the appropriate side.

Hoyer's district is just outside Washington, D.C., where he represents a substantial number of contractors and those who work for contractors.

“The issue of contracting ought to be on the merits of the contractor's application and bid and capabilities,” Hoyer said.

A liberal group, Public Campaign Action Fund, sent letters to a handful of Republican committee chairmen questioning their motives.

"The irony of these GOP chairmen opposing the president's planned executive order on disclosure is remarkable, especially considering every single day they are implicated in the same sort of quid pro quo they are so concerned about happening in the procurement process," David Donnelly, national campaigns director for the group said in a statement. "If these members think that money only influences the executive branch, they all need to look in the mirror."

The group said the biggest career contributor to Issa are the employees and political action committee of SAIC, a company which received $1.6 billion in federal government contracts in 2009.

Among the other examples cited by the group: Honeywell contributed $15,000 to Rep. Dan Lungren, chairman of the House Administration Committee, in 2010 and received $673 million in federal contracts in 2009.

Lockheed Martin has donated $122,150 to Rep. Buck McKeon, chairman of the Armed Services Committee, during his career and received at $14.5 billion in federal contracts in 2009.

Fox News' Chad Pergram contributed to this report.