House GOP plans another Obamacare vote on shutdown deal NEW: GOP Rep. Grimm says a "slight" shutdown may happen House to vote on one-year delay of Obamacare, scrapping medical device tax President Obama and Senate Democrats reject GOP bids to undermine Obamacare Senate Democrats restored funding for Obamacare opposed by Republicans Washington (CNN) -- With a possible government shutdown looming, House Republicans planned votes Saturday on a spending plan that also would delay Obamacare for a year and wipe out its tax on medical devices in defiance of threatened rejection by Senate Democrats and President Barack Obama. The decision that emerged from a rare weekend GOP caucus meeting called by House Speaker John Boehner increased the chances for at least a brief shutdown of the government starting Tuesday. A source inside the GOP meeting said the leadership received unanimous support for the plan, accentuated by cheering and clapping. House Republicans hold a solid majority and can push through the amendments in their attempt to pressure Senate Majority Leader Harry Reid and his Democratic majority to give in as the shutdown deadline approaches with the end of the fiscal year on Monday. Reid has warned that any changes to the Senate measure by the House would result in at least the start of a government shutdown because of the time it would take to reconsider the proposal. Republican Rep. Michael Grimm of New York said Saturday a "slight" shutdown could occur due to the little time left to pass a short-term spending plan for the new fiscal year that starts Tuesday. "I'm hoping no, but just look at the timing," Grimm said, laying out a scenario in which the political wrangling leads to likely last-minute deliberations on Monday and beyond. Boehner convened his caucus on Saturday to forge a counteroffer to the Senate's version of the spending plan, which restored funding for Obamacare that House Republicans had eliminated in their initial proposal. A statement by Boehner and other House GOP leaders said Saturday's votes would be on "two amendments to the Senate-passed continuing resolution that will keep the government open and stop as much of the president's health care law as possible." One amendment would delay full implementation of Obamacare for a year, and another "permanently repeals" the medical device tax that the statement said was "sending jobs overseas." Showing that the House Republicans don't expect the Senate to accept their changes, the leaders' statement said a separate vote Saturday would ensure that the military gets paid in the event of a government shutdown. Senate Democrats have said they will reject any changes to the spending plan by the House. A statement Saturday by Sen. Patty Murray of Washington, who chairs the budget committee, said House Republicans now were "actively pushing for a completely unnecessary government shutdown." Meanwhile, the White House made clear on Saturday that Obama dismisses any effort to tie provisions undermining Obamacare to the spending measure needed to prevent a government shutdown. A White House official referred CNN to Obama's statement Friday on the issue, saying "I don't think the president could have been any more clear." "As I've said before, if Republicans have specific ideas on how to genuinely improve the law, rather than gut it, rather than delay it, rather than repeal it, I'm happy to work with them on that through the normal democratic processes," Obama said Friday. But that will not happen under the threat of a shutdown. The legislative hot potato in Washington involves the spending plan known as a continuing resolution that is needed to keep the government funded past the end of the current fiscal year on Monday. On a strict party line vote, the Senate voted Friday to restore the Obamacare funding that the House had earlier eliminated. A similar 54-44 Senate vote then sent the measure back to the House, leaving Boehner with the choice of urging his divided Republican caucus to join Democrats in passing the Senate plan or to yield again to the tea party wing that seeks to undermine Obamacare. The amendments the House will consider Saturday also would fund the government until December 15, a month longer than the Senate version. Meanwhile, Democrats facing re-election next year in conservative-leaning states such as Mark Pryor of Arkansas, Mark Begich of Alaska, Mary Landrieu of Louisiana and Kay Hagan of North Carolina all resisted Republican pressure to buck their party over the Obamacare funding. Responding to the GOP tactics, Obama said Friday that new exchanges for private health insurance under the reforms will open next week as scheduled -- even if there is a government shutdown. The revised spending measure approved by the Senate -- called a continuing resolution -- would fund the government through mid-November, more than six weeks into the new fiscal year. Democratic Sen. Barbara Mikulski of Maryland said the goal now was to work out a broader spending plan for the rest of fiscal 2014 that would ease the impact of forced cuts to the military and other government programs. The tea party opposition to the Senate version would mean it could only pass the House with support from all Democrats and some Republicans, which would further weaken Boehner's already shaky leadership of his caucus. More moderate Republicans, such as veteran Sens. John McCain of Arizona and John Cornyn of Texas, criticize the strategy of tying a government shutdown to undermining the health care reform law passed by Democrats in 2010 and upheld by the Supreme Court last year. "There are some people across America that are so upset with Obamacare -- and I understand their frustration -- that they say we ought to shut down the federal government," Cornyn said, adding that the Congressional Research Service had determined the health care reforms would be funded even if there was government shutdown "because there are alternate sources of revenue that could be used to keep it going." Democratic Sen. Tom Harkin of Iowa called on House Republicans to "be responsible and forget about kids' games like picking up their marbles and going home or throwing a temper tantrum or shutting down the government because you can't get your way." The shutdown showdown comes a few weeks before another fiscal deadline -- the need to raise the nation's debt ceiling so the government can pay all its bills. Treasury Secretary Jack Lew said this week the limit on how much the government can borrow must be increased by October 17 or the nation could be technically in default. However, Boehner faces the same rift in his caucus over the debt ceiling issue, with tea party conservatives pushing for to undermine Obamacare and fulfill other Republican priorities in return for what Obama calls the responsibility of Congress to make sure America can pay its bills. On Thursday, Boehner had to delay introducing a GOP debt ceiling plan after conservatives complained the proposed package failed to include enough budget cuts and significant changes to entitlement programs. The initial proposal by House GOP leaders, which would raise the debt ceiling for a year, included a one-year delay of Obamacare, provisions to roll back regulations on businesses, tax reforms, and approval of the Keystone XL oil pipeline. CNN's Dana Bash, Jim Acosta, Lisa Desjardins, Ted Barrett and Deirdre Walsh contributed to this report.