A top Senate Democrat said Wednesday he doesn't think there is a "consistent position" by his party's leadership to vote against every piece of legislation brought to the floor simply to protest the partial government shutdown.

On Tuesday, Senate Democrats blocked a bipartisan, pro-Israel bill because they said they'd vote down any bill that doesn't reopen the government.

Sen. Bob Menendez, D-N.J., who was one of a handful of Democrats who voted with Republicans, said he would have done otherwise if he was aware of a long-term strategy.

"If we are going to have a consistent position that we'll vote against everything regardless of what it is ... I'm on board for that," he said on CNN.

"But I do not deduce from my colleagues yesterday that there is going to be a continuing no on everything and so this is a package I worked hard on as the ranking Democrat on the Senate Foreign Relations Committee that I think is important to national security. I would have voted no if I was convinced we were going to vote no on everything."

Schumer and other Senate Democratic leaders led the effort to block cloture on the Middle East security legislation.

Some Democrats, particularly Sens. Chris Van Hollen and Ben Cardin, both from Maryland where many federal employees impacted by the shutdown live, have urged their colleagues to "block" consideration of all bills not related to the partial government shutdown.

Senate Majority Leader Mitch McConnell, R-Ky., has said he won't bring any spending legislation that is opposed by the White House to the Senate floor.