Updated: 2:06 p.m.

With House passage of the bipartisan JOBS Act, Democrats and Republicans are trying ensure they get the credit they feel they deserve.

The bill, put together by House Majority Leader Eric Cantor (R-Va.), cleared the chamber today 390-23. Tagged as a job creation measure, the bill — formally known as the Jumpstart Our Business Startups Act — is designed to help small businesses raise capital.

The Senate is working on its own version of the measure, and Senate Democratic leaders hope to clear their package after the Senate Banking Committee finishes drafting it. President Barack Obama also supports the measure.

But despite the overwhelming bipartisan support, Democrats and Republicans are still tussling over who should get primary credit for the measure.

The Cantor package is made up of six existing bills, some which had Democratic sponsors and had passed the House with heavy Democratic support. A Cantor aide said the Majority Leader had identified small-business capital formation as a possible area of bipartisanship in a memo he released in September.

But Senate Democrats see Cantor’s move as a victory for them and an effort to work with Democrats on their initiatives. They note that the capital formation initiatives were part of a White House white paper released in January and chalk up the turn of events to House Republicans failing to win public support for their effort to roll back government regulations.

“They were losing the message [war] so they just bundled together a bunch of bipartisan bills that were independently already in the works,” said a senior Senate Democratic aide, who added that the deregulation bills were seen as ideological measures.

A House Republican aide said that the JOBS Act is just another piece of the party’s overall strategy to revitalize the economy, which includes rolling back burdensome regulations.

“Everyone understands that reducing red tape and eliminating barriers is an important part of creating jobs,” the aide said.

The Senate Democratic aide said the base measure of House package, which is sponsored by Reps. Stephen Fincher (R-Tenn.) and John Carney (D-Del.), was introduced Dec. 8 and was passed by House Financial Services Committee last month 54-1.

That provision of the package would reduce the costs of going public by phasing in certain regulations over a five-year period. The aide said that Sens. Charles Schumer (D-N.Y.) and Pat Toomey (R-Pa.) introduced the Senate version of the bill Dec. 1.

Cantor touted the proposal as a significant bipartisan achievement and noted that the House action shows that even in an election year, legislative victories are possible.

In an effort to highlight Senate inaction on other House bills Republicans argue would help create jobs, Cantor today called on Senate Majority Leader Harry Reid (D-Nev.) to pass the measure.

“Let’s build on this bipartisan momentum,” Cantor said before the House vote. “This week, President Obama offered his support for the JOBS Act. I strongly urge Senator Reid to take up this bill as quickly as possible and let’s get it to the president’s desk.”

Things got tense during debate in the House on Wednesday, when House Financial Services ranking member Barney Frank (D-Mass.) said it was a “shameful … cheap maneuver” for House GOP leaders to include a measure introduced last week by Rep. Ben Quayle (R-Ariz.) in the package. It would allow community banks to avoid registering with the Securities and Exchange Commission and bears a striking similarity to legislation by Rep. Jim Himes (D-Conn.) that the House passed 420-2 in November.

Frank said the bill had been “kidnapped along the way and brought here under another Member.”

Both bills contain identical provisions to increase the number of shareholders that a community bank can have before being required to register with the SEC. But Quayle’s bill does not require a study of the subject.

Rep. Jeb Hensarling (R-Texas) said the policy has bipartisan support regardless of who brings it to the floor.

“President [Ronald] Reagan once said that there is no limit to what the American people can accomplish if we don’t mind who gets the credit,” Hensarling said. “We appear to hear the ranking member say, ‘If I and my friends can’t take credit, we are going to pick up our toys and go home.’ All of us can take credit if we support the JOBS Act.”

Frank fired back. “For the gentleman from Texas, being part of the leadership that engaged in that shameful maneuver, to now accuse us of being excessively concerned with credit is the most hypocritical and dishonest statement I have ever heard uttered in this House,” he said.

Hensarling took umbrage and had the comments struck from the record under House rules regarding inappropriate words.

House Democrats also sought to downplay the significance of the bill’s passage.

Rep. Carolyn Maloney (D-N.Y.) said Wednesday that while she supports the measure “it does not really do a great deal to create more jobs, which we need.”

Likewise, House Minority Leader Nancy Pelosi (D-Calif.) was critical today.

“Instead of working together on a transportation bill, which is one of the biggest jobs initiatives Congress [has], Republicans are once again bringing to the floor some bills that we passed on the floor overwhelmingly,” she said at a press conference.

Referring to the package touted by Republicans, Pelosi declared, “They are jobs bill-light.”

Jessica Brady contributed to this report.