Minnesota Republicans Erik Paulsen and John Kline have rejected Democratic calls to sign a petition to force a straight up-or-down vote in the U.S. House to reopen the federal government, now in its eighth day of shutdown.

While President Obama appealed Tuesday to "reasonable Republicans," House Democrats have embarked on a longshot strategy to force a vote through a parliamentary maneuver called a "discharge petition." It would require the signatures of 218 House members to override the opposition of House Speaker John Boehner and the GOP leadership.

Democrats, a minority in the House, say they could produce about 200 of the needed votes. But breaking the logjam would require another 18 or so Republicans to defy their party's leaders, who have made blocking the implementation of the President Obama's health care overhaul a condition of funding the government.

Kline has remained silent on the prospect of a "clean," no-strings-attached vote on funding the government. Paulsen has said he would be willing to consider it, making him one of an estimated 20 House Republicans possibly willing to do so. (Paulsen's stance has also drawn protests from more conservative Republicans in Minnesota).

Rep. Michele Bachmann, the only other Minnesota Republican in the House, is not on anybody's list of wavering Republicans who might be willing to drop the GOP's demands for defunding or delaying Obamacare.

Obama also called on Boehner Tuesday to hold a vote on reopening the goverment without conditions.