House Majority Leader Eric Cantor (R-Va.) made a push for his signature 20 percent tax cut for small businesses during a brief news conference at the White House today.

Following a Rose Garden ceremony where President Barack Obama signed the Virginia Republican’s JOBS Act into law, Cantor said he didn’t get a chance to pitch Obama directly on the tax cut but added that he hopes the JOBS Act success is repeated.

“I hope it represents the kind of bipartisan work that we can actually accomplish here in Washington over the next few months,” said Cantor, who stood directly behind Obama when the president signed the bill into law.

“We have a very difficult economic situation still,” Cantor added. “The president said today that he’s always believed that it’s the private sector that’s the jobs generator in this country. I agree with him, and I think most Americans agree with him.”

That’s why, Cantor said, the House will move forward on the tax cut bill.

And he pushed back on criticism earlier today from Sen. Charles Schumer (D-N.Y.), who ripped Cantor’s proposal for giving money to wealthy business owners whether or not they create jobs. Schumer pushed for a Democratic alternative that would reward businesses for new hires and growth.

“I’m glad that the Senate is actually talking about finally doing something to help small-business people,” Cantor said.

But he said the tax cut shouldn’t come with strings attached for small-business owners.

“For the government to sit here and mandate that they act one way or another, in terms of hiring people or not, or who to hire, that just puts more restrictions on small business,” Cantor said.

“If we believe in free markets, if we believe that small businesses really are the growth engine, we ought to just empower them by allowing them to keep more of their money so they can retain and hire more workers,” he added.

Cantor took three questions at the brief news conference outside the White House and pushed for action on gas prices and other issues.

Earlier, during the seven-minute Rose Garden ceremony on the JOBS Act, Obama defended the bill as one that would remove burdens from companies seeking funding from the public. Although the law has been criticized for deregulating companies with up to $1 billion in revenue, Obama said that by encouraging those companies to go public, they would still face greater scrutiny. And he said the Securities and Exchange Commission would oversee the new law to ensure people aren’t taken advantage of, and he urged lawmakers to fully fund the SEC and other regulatory agencies so they can do so.