Yes the headline itself is phoney. It seems to be based on the simplicity that if GOP candidates generally, and executives/officials, are not pushing abolishment of the IRS publicly then they are not in favor of it. However, candidates are not pushing it as some 60+% of the public are against the idea.
in yours illustrating IRS funding cuts starts in 2010. Guess what date the Fair Tax Act which would remove the IRS was introduced in the GOP House? Yup, 1999.
The legislation would remove the Internal Revenue Service (after three years), and establish Excise Tax and Sales Tax bureaus in the Department of the Treasury. The states are granted the primary authority for the collection of sales tax revenues and the remittance of such revenues to the Treasury. The plan was created by Americans For Fair Taxation, an advocacy group formed to change the tax system. The group states that, together with economists, it developed the plan and the name "Fair Tax", based on interviews, polls, and focus groups of the general public. The FairTax legislation has been introduced in the House by Georgia Republicans John Linder (1999–2010) and Rob Woodall (2011–2014),[17] while being introduced in the Senate by Georgia Republican Saxby Chambliss (2003–2014). .. http://en.wikipedia.org/wiki/FairTax
Whoever put that headline in would have to deal with the suggestion that, if your heading is true then the GOP have been pushing a phony campaign for 16 years. And we know GOP wrong-mindedness and mean is not phoney. So, yup, fact check on yours is True.