House Majority Leader Eric Cantor (R-Va.) vowed to bring forward more piecemeal spending bills Thursday, as he expressed confidence President Obama would eventually be forced to negotiate.

In a memo sent to House Republicans, Cantor called the Democratic position “untenable” and “unsustainable,” adding that a steady diet of narrow funding bills would force Democrats to deal.

“I am confident that if we keep advancing common-sense solutions to the problems created by the shutdown that Senate Democrats and President Obama will eventually agree to meaningful discussions that would allow us to ultimately resolve this impasse,” he wrote.

“The American people … expect us to work together and they will not countenance one party simply refusing to negotiate.”

Cantor said Republicans are in an “unprecedented place,” and noted that during the last shutdown, President Clinton was “actively engaged” in searching for a solution.

While Congress’s top four leaders met with the president Wednesday evening, participants came out of the meeting saying the president was sticking with his stance of not negotiating on ending the shutdown and raising the debt limit.

In recent days, House Republicans have advanced several bills targeting high-profile areas of the government impacted by the shutdown, such as national parks, veterans’ benefits and the National Institutes of Health.

In turn, they have pressed Senate Democrats to take up the measures and ensure that at least some portions of the government can be funded while the two sides search for a broader compromise.

Thus far, Senate Democrats and the White House have rejected that approach, pushing back on Republicans to accept a plan to fund the entire government at sequester levels.

“One can only speculate as to why President Obama and Congressional Democrats are not only refusing to negotiate but now refusing to support or provide the American people with relief from the government shutdown,” Cantor wrote.

“But I firmly believe their position is untenable. It is at odds with how even past Democratic Presidents have handled similar situations. I expect that in addition to these bills, we will consider other similar pieces of legislation to reopen critical operations of the federal government,” he added.

The government shutdown is the result of GOP efforts to attach provisions trimming the healthcare reform law and Democrats’ refusal to consider any changes to the law during the funding debate.

Cantor reiterated in his memo that the last House Republican offer to fund the government before the shutdown was “reasonable.”

That plan called for a one-year delay of the law’s individual mandate and a repeal of the traditional employer healthcare subsidies for members of Congress and their staff.

Sen. Chuck Grassley (R-Iowa) inserted a provision into the law forcing members and their staff on to the exchanges created by the law.

Republicans have argued the employer exemption amounts to special treatment, and Cantor called it one of several “sweet-heart deals.”