They say the entire government should be reopened, not just the parts that Republicans like.
Top Senate Democrat Harry Reid said Republicans "are trying to cherry-pick some of the few parts of government that they like."
The plan by House Republicans would also allow the government of Washington, D.C., to use its own taxpayer funds to provide services like garbage pickup.
The closure of national parks is among the most visible effects of the partial government shutdown. The GOP plan would reopen doors and visitors centres at iconic parks like Yosemite and Yellowstone and museums along the National Mall.