John Kasich is rejecting pressure from members of the Republican establishment who are calling on him to drop out of the presidential race.

"When we get to Pennsylvania, we get to New Jersey, Connecticut, Rhode Island--let me tell you, if I drop out, Donald Trump is absolutely going to be the nominee," the Ohio governor and presidential candidate warned his supporters at a town hall in Wisconsin on Wednesday.

Kasich said he doesn't believe Ted Cruz can win any of the East Coast nominating contests that are coming up on the primary calendar.

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Though he is far behind Donald Trump and Cruz in the GOP race, Kasich touted his victory in his home state of Ohio last week and mentioned that he almost won Vermont and finished second in Massachusetts.

Responding to claims from Mitt Romney and Jeb Bush that only Cruz is the best option to beat Trump, Kasich said he doesn't know what they're "calculating."

"I think I can compete in the process, and I think we can go to convention," said Kasich, who really wants a contested convention in July.

But some argue that because he's so far behind and yet still remains in the race, it's preventing the two-man race between Trump and Cruz from intensifying and is actually aiding Trump. That's exactly why 2012 GOP presidential nominee Mitt Romney voted for Cruz in Utah on Tuesday and why former Florida Gov. Jeb Bush, who dropped out of the race in February, endorsed Cruz on Wednesday.

"I think John Kasich would be the best nominee, but he doesn't have a chance," Sen. Lindsey Graham, R-South Carolina, said on MSNBC's "Morning Joe" on Thursday.

Graham, who dropped out of the Republican presidential race in December and who recently endorsed Cruz, said Kasich's problem is that he's "an insider in an outsider year and nobody seems to want to buy that."

"I think Ted would make it a competitive race," Graham added.

According to CBS News' latest count, Trump leads with 740 delegates, Cruz has picked up 462 and Kasich only has 143. Kasich would face several obstacles, however, from getting close to the nomination. The GOP, for example, has a rule that requires candidates to win the majority of delegates from eight states in order to qualify for the nomination.

On Tuesday, Kasich came in second in Utah with only 17 percent of the vote while Cruz won 69 percent. Kasich came in fourth place with only 10 percent in Arizona's primary, even falling behind Marco Rubio who recently dropped out of the race.

Meanwhile, a survey out Wednesday showed that while Kasich is not performing well in the primary battle, he would perform the best in the general election, beating both Hillary Clinton and Bernie Sanders in hypothetical match-ups.