With the congressional stalemate over the budget showing no sign of ending soon, House Democrats reached out to moderate Republicans on Thursday with an urgent pitch to unite and end the government shutdown.

After the House voted on another small temporary funding measure, House Democrats' budget chief, Rep. Chris Van Hollen, approached moderate Republican Rep. Peter King, R-N.Y., and a few other lawmakers outside the House chamber to discuss joining forces against Republican conservatives who are using the budget fight to derail Obamacare.

“The clock is ticking,” Van Hollen, D-Md., told King.

After the group dispersed, Van Hollen confirmed he had been “talking to them to see what their appetite would be for doing something jointly.”

“They said they would think about it,” Van Hollen said.

King has been one of the most outspoken House Republican moderates calling for a vote to reauthorize government funding without strings attached. Most of his colleagues, meanwhile, have insisted on pressing the fight against Democrats in an effort to eliminate or weaken the Affordable Care Act.

But there are enough moderate Republicans who agree with King to approve a funding measure and end the impasse were they to join with Democrats.

That dynamic, Van Hollen said, gave him hope that King and like-minded Republicans might consider such a path.

“The way forward has really not changed, the way forward is to have a vote on a clean continuing resolution that could get to the president’s desk immediately,” Van Hollen said. “You’ve heard a lot of people like Peter King say that they would vote for that.”