They can’t just defund bills already passed and signed into law. So long as Obamao is president, GOP can’t pass anything without a veto override which is impossible in senate.
Your understanding of the situation is very different from mine. Obamacare is not funded in years going forward. Each year Congress must pass a budget that authorizes spending for various programs. If they do not vote to fund something then it is unfunded. Thus there is no need for Congress to pass legislation and for Obama to sign it to de-fund Obamacare. They need only to not pass legislation funding Obamacare. The Republican House majority is sufficient to accomplish this. A spending bill that includes Obamacare funding need never reach the Senate.