Two US intelligence chiefs will begin a public lobbying campaign on Capitol Hill on Thursday, as they try to dissuade Congress from dismantling any part of the vast surveillance apparatus constructed in the aftermath of September 11 terrorist attacks.

Their appearance before the Senate intelligence committee comes a day after a group of Democratic and Republican senators proposed a package of comprehensive reforms to surveillance powers, including what would amount to a ban on the bulk collection of millions of records of telephone calls in the US.

The director of the National Security Agency, General Keith Alexander, and the director of national intelligence, James Clapper, have been involved in an intensive campaign, both public and behind the scenes, to prevent lawmakers from responding to disclosures by the whistleblower Edward Snowden with new legislation that would curb the powers of the intelligence establishment.

Alexander defended the mass collection of phone records earlier this week in a speech in Washington, in which he said the program had been used in some capacity during investigations into the Boston Marathon bombing, and in assessing possible threats against US embassies abroad.

Clapper has a history of controversial congressional experiences. In the aftermath of Snowden's disclosures he was forced to apologise for misleading Congress.

He had told a hearing of the Senate intelligence committee that the US did not wittingly collect data on millions of Americans, but a secret court document, disclosed by Snowden and published by the Guardian, proved the declaration to be untrue. James Cole, the deputy attorney general, who has defended US intelligence powers during previous congressional appearances, will also give testimony on Thursday.

On Wednesday, Ron Paul, the Republican senator who has joined three Democrats in backing the bill proposing reform of US surveillance activities, repeated his call on Clapper to resign. "I don't think you can come to a committee, and lie to a committee, and maintain your credibility," he said.

Paul and the Democratic senators Ron Wyden, Mark Udall and Richard Blumenthal unveiled their bill at a joint press conference, saying the package of measures represented wholesale reform and should be treated as the baseline for changes to the intelligence apparatus that are more than just cosmetic.

The White House is believed to be seeking more superficial changes, perhaps implementing tweaks to the secretive court process which oversees surveillance warrants and agreeing to greater transparency, but resisting concrete diminution in the powers currently bestowed upon the NSA and other intelligence agencies by the Patriot Act and the Fisa Amendment Act.

The administration has the support of the Democratic senator Dianne Feinstein, who chairs the intelligence committee and who has said she opposes ending the program for mass collection of phone records, even though, according to critics, the US intelligence establishment has failed to show where it has proved critical in terrorism investigations.

Wyden and Udall have been thorns in the side of the intelligence community, using their position on the committee, which permits them privileged access to classified briefings, to repeatedly challenge senior officials on the accuracy of their public testimony.

Patrick Leahy, the chair of the Senate judiciary committee, is pushing his own legislation, which looks likely to be less far-reaching than the bipartisan bill submitted on Wednesday night, but which would also prevent the NSA and partner agencies from collecting millions of phone records of Americans, irrespective of whether they are suspected of involvement in terrorism.

Few in Washington doubt that some kind of bill will be passed in the weeks or months ahead, in response to disclosures made by Snowden. The question is how profound those changes will be and whether more radical changes will be pushed through, against the wishes of the White House and leaders in the Senate and House.

The appetite in Washington for reform of surveillance programs was made apparent in July, when a House of Representatives proposal to effectively end the NSA's bulk collection of phone records was defeated by just 12 votes.

Rand Paul has joined three Democratic senators in backing surveillance reform. Photograph: Mark Lyons/EPA

A House alliance between libertarian Republicans and left-leaning Democrats is now being emulated in the Senate. Wednesday's press conference – featuring leftwingers Wyden, Udall and Blumenthal alongside Paul, one of the most prominent libertarians in the Republican party – suggested those dynamics could be repeated.

Wyden said on Wednesday the House vote in July had been "a huge wake-up call", revealing the depth of opposition to government surveillance programs in the wake of Snowden's disclosures. Blumenthal said their bill represented a "coming together of a very diverse ideological elements of our respective parties".

Their bill, the Intelligence Oversight and Surveillance Reform Act, merges competing legislative proposals announced by the senators before the summer recess, and cherry-picks from ideas contained in about 12 other draft bills. It would prohibit the NSA's bulk collection of domestic phone records under section 215 of the Patriot Act, the most controversial aspect of US surveillance revealed by the NSA files.

The bill would also prevent a similar data trawl of internet communication records, which was stopped in 2011, and definitively close a so-called "backdoor" that potentially enables the NSA to intercept the internet communications of Americans swept up in a program protected by Section 702 of the of the Fisa Amendments Act.

There is limited, if any, support in Congress for limiting the NSA's ability to monitor or gather evidence on foreigners.

The bill fuses with a proposal originally made by Blumenthal, which aims to reform the Fisa court, making the quasi-judicial process more transparent and accountable.

If made law, the act would require a "constitutional advocate" to be introduced into the opaque court process, so the government could be challenged on privacy grounds in significant or precedent-setting cases. It would insert an adversarial dimension to a court process that is currently one-sided in favour of the government.

"The disclosures over the last 100 days have caused a sea change in the way the public views the surveillance system," Wyden said.