The war against the poor, which also has racial implications, is a very important part of Republican ideology. The Tea Party concern about federal budget deficits is really a smokescreen for a deeper issue. They want to cut federal safety net programs, including Obamacare, which disproportionally benefit minorities and immigrants who tend to vote for Democrats.
The GOP base consists of a relatively small number of well off voters who do care about fiscal policy. They worry that their taxes may have to be raised in order to fund entitlement programs that absorb a rising share of federal spending. They also support immigration reform which is anathema to Tea Partiers. The GOP cannot win elections, however, by appealing to their traditional base. They must also attract less well off voters to their cause. They like Social Security and Medicare, which establishment Republicans worry about, but they don't like immigrants and they don't like to see their tax dollars going to the "wrong kind of people". They also place a high value on fundamental Christian and economic ideas which the Republican establishment gives lip service to as long as it differentiates them from liberal democrats who are portrayed as godless socialists.
This difficult marriage between establishment republicans and the Tea Party has helped the GOP to win the House, but it has harmed them in national elections and it has cost them some seats in the Senate where the Tea Party succeeded in nominating candidates who were unelectable. The real question going forward is whether the marriage can be saved as it is or whether it will fail. A republican leader like Ted Cruz, who is admired by the Tea Party, might be able to engineer a takeover of the GOP or he might successfully create a third party.