The healthcare bill crafted by House Democrats will require a new $800 billion in taxes, Rep. Paul RyanPaul Davis RyanGOP leaders pitch children's health funding in plan to avert shutdown Lawmakers see shutdown’s odds rising Fix what we’ve got and make Medicare right this year MORE (R-Wisc.) alleged Wednesday.

Ryan, the ranking member of the House Budget Committee, asserted that a Congressional Budget Office (CBO) "scoring" of the House Democrats' bill would show a need for much higher taxes.

"We will get the score, we think, from the Democrats after the July 4th recess, meaning in about a week and a few days," he said on CNBC. "They're going to need about $800 billion at least in higher taxes -- we're probably going to see a little bit more than that."

Republicans have hammered away at the majority party's plans for both its cost and what they say is expansiveness. Ryan is one of the few GOP lawmakers, though, to allege a specific amount of new taxes needed.

Rep. Frank Pallone (D-N.J.) said this morning on CNBC as well that the House Democrats' plan would include more Americans than the Senate version, which the CBO initially priced around $1.6 trillion. Pallone said the House bill would cover more for less of a cost -- paid for primarily to cuts in reimbursement rates and other savings.

Ryan said that the Democratic bill may need to be paid for by a "grab bag" of different tax increases, or other specific taxes.