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Washington (CNN) - A day after the White House claimed victory in its Obamacare enrollment numbers, the group tasked with electing Democrats to the House acknowledged it's still a "tough climate" for Democrats in this year's midterms, but also insisted they still plan to campaign on the health care law.

But Rep. Steve Israel, chairman of the Democratic Congressional Campaign Committee, said an even bigger focus this year will be renewed attempts by Democrats to clobber Republican Rep. Paul Ryan's budget plan on the campaign trail.

Speaking at the National Press Club on Wednesday, Israel said Democrats are "ratcheting up" their offense against Republicans who favor a repeal of the health care law, and stressed that Democratic strategy will focus on the negative consequences of eliminating the law.

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Israel faulted Republicans for maintaining an "obsessive" and "relentless" assault against the Affordable Care Act. Obamacare is "the only thing that animates a fractured, weak base that is in a civil war," he said, referring to the GOP.

But Israel didn't suggest there'd be party-wide Democratic support for the health care law. As some candidates or incumbents in tight races have distanced themselves from President Obama-whose approval ratings have remained underwater this year-Israel acknowledged that some Democrats will need to continue doing what's best for their contests.

"Every member has to be a good fit for their district. When you have a disagreement with the President, you should state your disagreement. When you have an agreement with the President, you should state your agreement," he said. "Don't worry about what's happening inside the Beltway. Worry about what's happening when you go door to door."

The priority, he said, will be bashing Ryan's budget plan, which balances the federal budget in a decade in part by repealing Obamacare, changing Medicare and cutting social programs like food stamps.

"Let me give the three words that will define the next seven months: The Republican budget," Israel said.

Democrats argue that Ryans budget places too much of a burden on the middle class, while allowing tax breaks for the wealthy.

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Democrats to focus on Ryan budget in 2014